The words, "our righteousness" appear together only six times in the Bible, and all of them are found in the Old Testament (Deut. 6:25; Isa. 64:6; Jer. 23:6; 33:16; 51:10; Dan. 9:18). But amazingly, these six set the stage for what is coming in the New Testament.
First, we learn that we will have our own righteousness (the right to stand confidently before God) IF we obey ALL the commandments of God. "And it shall be our righteousness, IF we observe to do ALL these commandments before the LORD our God, as He hath commanded us (Deut. 6:25). Because we cannot always obey God, the Apostle Paul states that ALL of us are sinners needing salvation (Rom. 3:23).
Secondly, because we do not always obey God, "...we are ALL as an unclean thing, and ALL our righteousnesses are as filthy rags; and we ALL do fade as a leaf; and our iniquities, like the wind, have taken us away (Isa.64:6). In other words, because our efforts to be holy are doomed to failure, we face the inevitable: death (Rom. 6:23a).
Thirdly, since we are incapable of living a holy life before our Creator, and therefore have no righteousness of our own, God has offered us the free gift of His righteousness. Jeremiah tells us that those who will believe and accept His gift, will call God, "THE LORD OUR RIGHTEOUSNESS" (Jer. 23:6; 33:16). Paul said it this way: "For He hath made Him to be sin for us, Who knew no sin; that we might be made the righteousness of God in Him 2 Cor. 5:21). Yes, "The LORD hath brought forth our righteousness: come, and let us declare in Zion the work of the LORD our God (Jer. 51:10).
Finally, when we believe that the Father sent His Son to take our sin and give us His own righteousness, we, being aware that there is nothing we can do to become righteous, no longer live out of fear of God's judgment, but we are totally motivated by our gratitude for what He has done for us.
Daniel wrote, "O my God, incline Thine ear, and hear; open Thine eyes, and behold our desolations, and the city which is called by Thy name: for we do not present our supplications before Thee for our righteousnesses, but for Thy great mercies" (Dan. 9:18).
Paul, after presenting the "Romans Road" (Rom. 3:23; 6:23a; 5:8; 6:23b; 10:9-10), says, "I beseech you therefore, brethren, by the mercies of God, that ye present your bodies a living sacrifice, holy, acceptable unto God, which is your reasonable service. Having no righteousness of our own, we show our gratitude to Him for He is THE LORD OUR RIGHTEOUSNESS.