Righteousness is a work, one which Jesus has Finished for us:
"It is Finished." (John 19: 30)
"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 Corinthians 5: 21)
The original Hebrew bears out something more active regarding the effects of Christ in us, our hope of glory (Colossians 1: 27), and our righteousness (1 Corinthians 1: 30):
"Effect" means "Service" or even "Bondage". Righteousness works for us.
Why is this the case?
The New Covenant outlines what God is going to do for us:
"10For this is the covenant that I will make with the house of Israel after those days, saith the Lord; I will put my laws into their mind, and write them in their hearts: and I will be to them a God, and they shall be to me a people:
11And they shall not teach every man his neighbour, and every man his brother, saying, Know the Lord: for all shall know me, from the least to the greatest.
12For I will be merciful to their unrighteousness, and their sins and their iniquities will I remember no more." (Hebrews 8: 10-12)
How is that Lord no longer remembers our sins? Every sin of the world -- past, present, and future -- was remembered in the Body of His Son Jesus Christ:
"10By the which will we are sanctified through the offering of the body of Jesus Christ once for all." (Hebrews 10: 10)
"For Christ also hath once suffered for sins, the just for the unjust, that he might bring us to God, being put to death in the flesh, but quickened by the Spirit:" (1 Peter 3: 18)
"But if we walk in the light, as he is in the light, we have fellowship one with another, and the blood of Jesus Christ his Son cleanseth us from all sin. 8If we say that we have no sin, we deceive ourselves, and the truth is not in us. 9If we confess our sins, he is faithful and just to forgive us our sins, and to cleanse us from all unrighteousness. 10If we say that we have not sinned, we make him a liar, and his word is not in us." (1 John 1: 7-10)
Through Jesus' blood, we are cleansed from all sin, we are cleansed from all unrighteousness. This gift of righteousness is the enforcing clause of the New Covenant, so that God indeed can be a "God"
Because of what Jesus did at the Cross, God is bound to bless us, because His Son paid with His life and blood that with Him, we may receive all things (Romans 8: 31-32)