Robert Haldane said of this passage
"This righteousness is also said to be of God by faith-- that is sinners become partakers of it by faith. The righteousness of God, then, is not a method of justification, but the thing itself which God has provided, and which He [gives it] through faith. The Gospel is the power of God unto salvation, because it reveals God’s righteousness, that righteousness which fulfils the demand of His law, which His justice will accept, and which is upon all them that believe."
What a glorious thought, the imputed righteousness of Christ! Oh that we could grasp being "in Christ" - what joy, what peace that would bring.
Many mistake the Old Testament as being a covenant of works for salvation however nothing could be further from the truth.
Jer 33:14-16 Behold, the days come, saith the LORD, that I will perform that good thing which I have promised unto the house of Israel and to the house of Judah. In those days, and at that time, will I cause the Branch of righteousness to grow up unto David; and he shall execute judgment and righteousness in the land. In those days shall Judah be saved, and Jerusalem shall dwell safely: and this is the name wherewith she shall be called, The LORD our righteousness.
The LORD our righteousness. Our own righteousness being filthy rags, dung, worthless and vile being taken away, and by faith, receiving the righteousness of Christ making Jesus the Lord OUR righteousness. I have righteousness, but not mine, His imputed to my account that I am reckoned as righteous in the sight of God, that I will be presented in the courts of Heaven guiltless, blameless, perfect in His sight.