The righteousness of God is his own character or integrity.  Without any other consideration it would mean damnation for all sinners without exception, but Paul speaks of it in terms of the covenantal promise so that the righteousness of God is not merely a source of fear for sinners but a source of hope and faith for believing sinners.

We see this plainly in Romans 3.1-6 where the righteousness of God is God’s own character and correlates to his faithfulness:

“Then what advantage has the Jew? Or what is the benefit of circumcision? Great in every respect. First of all, that they were entrusted with the oracles of God. What then? If some did not believe, their unbelief will not nullify the faithfulness of God, will it? May it never be! Rather, let God be found true, though every man be found a liar, as it is written, “That Thou mightest be justified in Thy words,/ And mightest prevail when Thou art judged.” But if our unrighteousness demonstrates the righteousness of God, what shall we say? The God who inflicts wrath is not unrighteous, is He? (I am speaking in human terms.) May it never be! For otherwise how will God judge the world?”

This is confirmed by the references to God’s righteousness both before and after this passage.  First, in Romans 1.16-18 we see Paul draw a parallel between the revelation of God’s righteousness and the revelation of God’s wrath–in both cases refering to aspect of his own character:

“For I am not ashamed of the gospel, for it is the power of God for salvation to everyone who believes, to the Jew first and also to the Greek. For in it the righteousness of God is revealed from faith to faith; as it is written, “But the righteous man shall live by faith.” For the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men…”

Notice also that Paul is drawing on Habbakuk with deals both with who will be vindicated by God and the question of how God himself can be righteous if he is doing or allowing certain things in history.

Following Romans 3.1-6 we see more confirmation in which the Righteousness of God is revealed in what he did in Jesus–He has kept his promises:

“But now apart from the Law the righteousness of God has been manifested, being witnessed by the Law and the Prophets, even the righteousness of God through faith in Jesus Christ for all those who believe; for there is no distinction; for all have sinned and fall short of the glory of God, being justified as a gift by His grace through the redemption which is in Christ Jesus; whom God displayed publicly as a propitiation in His blood through faith. This was to demonstrate His righteousness, because in the forbearance of God He passed over the sins previously committed; for the demonstration, I say, of His righteousness at the present time, that He might be just [righteous] and the justifier of the one who has faith in Jesus.”

We have here two parallel statements:
“the righteousness of God though faith in Jesus Christ”
“a propitiation in His blood through faith”

The righteousness or faithfulness of God was proven in the cross of Christ.  God manifested his righteousness by sending his son to die for our sins and then raising him for our justification.

Paul’s concept of the righteousness of God (and that of the NT in general, comes from the OT.  As Sinclair Ferguson wrote in his commentary on Daniel:

“Elijah had come to God and said, “Lord, You promised. I believe this is Your word. It must be so. Let it be so in answer to my prayers.” Daniel’s praying was of the same order as his appeal to the “righteousness” of God eloquently testifies (vv. 7, 16). The Old Testament term “righteousness” has a specifically covenantal orientation. The young Martin Luther could not see this when he struggled to understand what Paul meant by “the righteousness of God” (Rom. 1:17). Of course, Luther was not helped by the fact that his Latin Bible translated Paul’s Greek word dikaiosune (righteousness) as justitia (justice). Luther’s mistake has sometimes been repeated by evangelical Christians. Often righteousness has been thought of merely as the equivalent of the just punishment of God. Preachers therefore may often accompany the use of the phrase “the righteousness of God” with the gesticulation of a clenched fist. It is clear even from this passage, however, that this is to reduce the full biblical meaning of God’s righteousness. Daniel sees the righteousness of God both as the basis for God’s judgment of the people (v. 7) and also as the basis for his own prayer for forgiveness (v. 16). How can this be? In Scripture, “righteousness” basically means “integrity.” Sometimes it is defined as “conformity to a norm.” In the case of God, the norm to which He conforms is His own being and character. He is true to Himself, He always acts in character. God has expressed the norm of His relationship to His people by means of a covenant. He will always be true and faithful to His covenant and the promises enshrined in it. Plainly, God’s righteousness is His faithfulness to His covenant relationship (Sinclair Ferguson, Daniel (Waco, TX: Word Books, 1988).”

Consider for an example outside of Daniel, consider Isaiah 45.21-25

“There is no other God besides Me, A righteous God and a savior; There is none except Me. Turn to me and be saved all the ends of the earth; For I am God and there is no other I have sworn by Myself The word has gone forth from My mouth in righteousness and will not turn back, That to Me every knee will bow, every tongue will swear allegiance. They will say of Me, “Only in the LORD are righteousness and strength.””

Here in our passage, all the nations are called to abandon their many gods and many lords because these gods and lords cannot save. Why not? Why can’t they save their worshipers? Well, for one thing, they simply aren’t strong enough to save their people. Since these gods are, at most, mere creatures who are being given false honors, as Romans 1.23 tells us, they are not powerful enough to rescue their people. They are not capable of delivering anyone. Only in the LORD is strength: so He alone can save all the ends of the earth. But there is another reason why these false gods cannot save. They not only lack the strength; they lack the moral character. Even if they had the power to save their worshipers, they wouldn’t do it, no matter what promises they made. They are not trustworthy. They are not faithful. They are not righteous. Only in the LORD is righteous; so He alone can be trusted to save all the ends of the earth. Note that the phrase, “Only in the LORD are righteousness and strength” cannot be used to justify the doctrine of the imputation of Christ’s righteousness. Is strength imputed to us? No. The point of mentioning the LORD’s strength is that He is powerful enough to save His people. The issue in this passage is not what is imputed to God’s people, but God’s qualities which entail that He is trustworthy as a savior. God is a savior because he is strong–capable of saving His people. God is a savior because he is righteous–willing to save hie people. God’s righteousness assures us that He is our savior. His righteousness does not jeopardize our salvation, but guarantees it. He does not save us depite His righteousness but because of His righteousness.

We see this also in the Psalms.

Psalm 36.10 O continue Your lovingkindness to those who know Thee; And Your righteousness to the upright in heart.

Psalm 103.17 The lovingkindness of the LORD is from everlasting to everlasting on those who fear Him, And His righteousness to children’s children.

Psalm 88.11-12 Will Your lovingkindness be declared in the grave, Your faithfulness in Abaddon? Will Your wonders be made known in the darkness? And Your righteousness in the land of forgetfulness?

Psalm 98.1-3:

O sing to the LORD a new song, For He has done wonderful things, His right hand and His holy arm have gained the victory for Him. The LORD has made known His salvation; He has revealed His righteousness in the sight of the nations He has remembered His lovingkindness and His faithfulness to the house of Israel; All the ends of the earth have seen the salvation of our God.

Notice that this is exactly what Paul echoes in Romans 1.16-17 in the context of his call to preah the Gospel to all nations.  He is revealing God’s righteousness by telling of God’s ultimate righteous act.

Isaiah says the same thing:

Isaiah 45.8 Drip down, O heavens, from above, And let the clouds pour down righteousness; Let the earth open up and salvation bear fruit, And righteousness spring up with it. I the LORD have created it.

Isaiah 46.12-13 Listen to Me, you stubborn-minded, Who are far from righteousness. I bring near My righteousness, it is not far off; And My salvation will not delay. And I will grant salvation in Zion, My glory for Israel.

Saving Israel, giving Israel glory, is a manifestation of God’s righteousness. So if God’s salvation is near then God’s righteousness is near–in other words, it is about to be revealed.

Isaiah 51.6b But My salvation shall be forever, And My righteousness shall not wane.

Isaiah 51.8b But My righteousness shall be forever, And My salvation to all generations.

Isaiah 56.1 Thus says the LORD, Preserve justice, and do righteousness, For My salvation is about to come And My righteousness to be revealed.

Notice that this is the General view of Paul in other letters as well as in other NT writers

First John 1.9 If we confess our sins, He is faithful and righteous to forgive us our sins and to cleanse us from all unrighteousness.

First Peter 2.18-23 Servants, be submissive to your masters with all respect, not only to those who are good and gentle, but also to those who are unreasonable. For this finds favor, if for the sake of conscience toward God a man bears up under sorrows when suffering unjustly. For what credit is there if, when you sin and are harshly treated, you endure it with patience? But if when you do what is right and suffer for it you patiently endure it, this finds favor with God. For you have been called for this purpose, since Christ also suffered for you, leaving you an example for you to follow in His steps, who committed no sin, nor was any deceit found in His mouth; and while being reviled, He did not revile in return; while suffering, He uttered no threats, but kept entrusting Himself to Him who judges righteously.

Second Timothy 4.6 I have fought the good fight, I have finished the course, I have kept the faith; in the future there is laid up for me the crown of righteousness, which the Lord, the righteous Judge, will award to me on that day; and not only to me, but also to all who have loved His appearing.

In each of these three cases, God’s righteousness, in Peter and Paul his righteousness as a judge, is grounds not for despair but for hope and confidence of an eventual deliverance and vindication. For John, it means one can be assured of forgiveness.

How this can be true when God is dealing sinners is explaine in Romans 4-5 and elsewhere.  Only by virtue of the imputation of the righteousness of Christ can sinners possibly stand before God.  But this term is not to be imported into Paul’s phrase “the righteousness of God.”  When Paul does speak of a righteousness being imputed by God he uses a different phrase: “righteousness *from* God” (“dikaiosune ek theou”–Philippians 3).  That phrase is not the same as the one he uses in Romans: “the righteousness of God” (“dikaiosune theou”).

I further note that the Westminster Confession nor Catechisms use the term “the righteousness of God” or dictate any understanding of that expression.

Finally, one needs to remember that the close proximity of references to God’s righteousness and those to justification are perfectly understandable without any notion of a transfer of “righteousness” from God to the sinner. (I repeat: I am not denying that Jesus’ righteous status is shared with His people. It most certainly is. I am simply denying that Paul is speaking of such imputation in these specific passages by the use of this specific term.)

Consider Psalm 35.24: “Judge me, O LORD, according to Thy righteousness.” Though two different word groups are used, the Psalmist is plainly asking for justification and believes it will be given to him on the basis of God’s righteousness. But there is no transfer imagined here. The point is that God’s character and integrity guarrantee that he will vindicate those who belong to him.

Likewise, in Isaiah 45.24, 25, the righteousness of God means he can be trusted to fulfill his promise so that “all the offspring of Israel” will be “justified.” (Regarding the two different word roots for “judgment” and “justification,” one should note that these are both present in Romans 2 and 3 and thus the forensic meaning of justification is, in part, established by the courtroom language of “judgment” use in those chapters. Of course, God’s righteousness also demands that sinners be punished. Romans 3.21-26 acknowledges this fact. What makes God’s righteousness a basis for hope for sinners, instead of fear, is that God made a covenant to deal with sin and justify sinners who entrust themselves to him. God’s righteousness demands that He keep His promises as well as punish sin.