One of the most helpful commentaries on the Book of Romans, in my opinion, is Jack Cottrell’s College Press NIV Commentary on Romans (College Press Publishing Company, 2005). His explanation of the phrase “the righteousness of God” and its meaning in Romans 1:17 is a great example of his clarity of insight.
Specifically what is this righteousness of God, this gift of God’s grace that is revealed in the gospel? We know that God imparts a righteous character to us through the gift of the Holy Spirit received in Christian baptism, so that we actually become more and more righteous, more and more holy as we mature in our faith. But it is generally agreed that “the righteousness of God” in 1:17 is not this imparted righteousness, but is rather an imputed righteousness, i.e., a righteousness established by someone else (Jesus Christ) and set down to our account and counted as our own. It results not in a righteous character; this comes from the Holy Spirit’s working in us. It results rather in a righteous status. This righteous status is the state of being justified. Justification is thus not equivalent to the righteousness of God, but is the result of it (p. 118).