I preached from this text this past Sunday and had to wrestle (as have many before me) with the meaning of the phrase “the righteousness of God.” Douglas Moo, in his superb commentary on Romans (in the NICNT series), points out that the term “righteousness of God” undergoes a subtle change in meaning between Rom. 21-22 and Rom. 25-26 (see Moo, p. 219).
In Rom. 3:21-22, the phrase”righteousness of God” refers to God’s “eschatological justifying activity” by which God “empowers the gospel to mediate salvation to sinful human beings (Cf. Rom. 1:16-17). In other words, the righteousness by which God justifies the sinner. This justification is apart from the law and only through faith in the finished work of Christ.
In Rom. 3:25-26, the phrase “righteousness of God” refers to “the ‘integrity’ of God, his always acting in complete accordance with his own character.” In other words, the righteousness of God’s own character that ensures that he does what is right. As Moo says, his “integrity.” This is why Paul says twice that God “demonstrates his righteousness,” he wants it to be clear that he has exacted payment for sin (and that he has only exacted one payment for sin). This is why Paul says that he is “just and the justifier.”
In a footnote (p. 219, n. 4), Moo says, “The jump from one to the other is not as great as might first appear, since always lurking in ‘righteousness’ language is allusion to the character and person of God.”
Moo acknowledges that “most contemporary exegetes and theologians reject this interpretation; but we are convincedthat this shift in meaning is required by the data of the text, and, indeed, gives to the text its extaordinary power and significance.”