Introduction: The following is a quick explanation of who is righteous today and how it is possible to say such a thing!

The Righteousness of the Lost:
Isaiah 64:6 - rags.  But we are all as an unclean thing, and all our righteousness are as filthy rags; and we all do fade as a leaf; and our iniquities, like the wind, have taken us away.
Romans 3:10 - there is none righteous. As it is written, There is none righteous, no, not one:
Romans 10:3,4 - have not submitted themselves to the righteousness of God.  For they being ignorant of God's righteousness, and going about to establish their own righteousness, have not submitted themselves unto the righteousness of God.  For Christ is the end of the law for righteousness to every one that believeth.

The Greater Commission
Romans 3:21   But now the righteousness of God without the law is manifested, being witnessed by the law and the prophets; ...

The Righteousness of the Saved:
We are made righteous - Romans 5:19 For as by one man's disobedience many were made sinners, so by the obedience of one shall many be made righteous.

Righteousness for Salvation
Romans 10:10 - the heart. For with the heart man believeth unto righteousness; and with the mouth confession is made unto salvation.
Titus 3:5 - not by my own... Not by works of righteousness which we have done, but according to his mercy he saved us, by the washing of regeneration, and renewing of the Holy Ghost;  Which he shed on us abundantly through Jesus Christ our Saviour;

Believe
To us ... Romans 3:22,23  Even the righteousness of God which is by faith of Jesus Christ unto all and upon all them that believe: for there is no difference: For all have sinned, and come short of the glory of God;
Submit to Christ ... Romans 10:3,4   For they being ignorant of God's righteousness, and going about to establish their own righteousness, have not submitted themselves unto the righteousness of God.  For Christ is the end of the law for righteousness to every one that believeth.
We are made ... II Corinthians 5:21 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.
Faith counted for righteousness ... Romans 4:5,6  But to him that worketh not, but believeth on him that justifieth the ungodly, his faith is counted for righteousness. Even as David also describeth the blessedness of the man, unto whom God imputeth righteousness without works,
Ephesians 1:12-14   That we should be to the praise of his glory, who first trusted in Christ.  In whom ye also trusted, after that ye heard the word of truth, the gospel of your salvation: in whom also after that ye believed, ye were sealed with that holy Spirit of promise,  Which is the earnest of our inheritance until the redemption of the purchased possession, unto the praise of his glory.

A gift
Romans 5:17-18  17: For if by one man's offence death reigned by one; much more they which receive abundance of grace and of the gift of righteousness shall reign in life by one, Jesus Christ.)  Therefore as by the offence of one judgment came upon all men to condemnation; even so by the righteousness of one the free gift came upon all men unto justification of life.
Made possible by the Jews ... Romans 11:11,20,22,25

So... It's  all Jesus Christ
It's His walk of the grace of God and the righteousness of Jesus Christ - Galatians 2:20,21   I am crucified with Christ: nevertheless I live; yet not I, but Christ liveth in me: and the life which I now live in the flesh I live by the faith of the Son of God, who loved me, and gave himself for me.  I do not frustrate the grace of God: for if righteousness come by the law, then Christ is dead in vain.
It's His words for instruction in righteousness - II Timothy 3:16,17  All scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness: That the man of God may be perfect, throughly furnished unto all good works.
John 16:13,14  Howbeit when he, the Spirit of truth, is come, he will guide you into all truth: for he shall not speak of himself; but whatsoever he shall hear, that shall he speak: and he will shew you things to come.  He shall glorify me: for he shall receive of mine, and shall shew it unto you.

Our walk should be His walk!
Put on the new man ... Ephesians 4:22-24 That ye put off concerning the former conversation the old man, which is corrupt according to the deceitful lusts; And be renewed in the spirit of your mind; And that ye put on the new man, which after God is created in righteousness and true holiness.
Paul tells us to follow after righteousness ...
I Timothy 6:11  But thou, O man of God, flee these things; and follow after righteousness...
II Timothy 2:22   Flee also youthful lusts: but follow righteousness...
We are to be servants of righteousness
Romans 6:13-19  Neither yield ye your members as instruments of unrighteousness unto sin: but yield yourselves unto God, as those that are alive from the dead, and your members as instruments of righteousness unto God.  For sin shall not have dominion over you: for ye are not under the law, but under grace.  What then? shall we sin, because we are not under the law, but under grace? God forbid.  Know ye not, that to whom ye yield yourselves servants to obey, his servants ye are to whom ye obey; whether of sin unto death, or of obedience unto righteousness?  But God be thanked, that ye were the servants of sin, but ye have obeyed from the heart that form of doctrine which was delivered you.  Being then made free from sin, ye became the servants of righteousness.  I speak after the manner of men because of the infirmity of your flesh: for as ye have yielded your members servants to uncleanness and to iniquity unto iniquity; even so now yield your members servants to righteousness unto holiness.
Romans 8:4  That the righteousness of the law might be fulfilled in us, who walk not after the flesh, but after the Spirit.

His righteousness is to be our breastplate
Ephesians 6:14  Stand therefore, having your loins girt about with truth, and having on the breastplate of righteousness;

Even Peter tells Jews (and us) to walk in it!
I Peter 2:24   Who his own self bare our sins in his own body on the tree, that we, being dead to sins, should live unto righteousness: by whose stripes ye were healed.

Someday, it will be everywhere...
II Peter 3:13  Nevertheless we, according to his promise, look for new heavens and a new earth, wherein dwelleth righteousness.

5:12: For thou, LORD, wilt bless the righteous; with favour wilt thou compass him as with a shield.

11:3: If the foundations be destroyed, what can the righteous do?
The Book is the foundation as well as Christ Himself - those are His words, and that is how we keep the 'foundation' from being destroyed!

11:7: For the righteous LORD loveth righteousness; his countenance doth behold the upright.

33:1: Rejoice in the LORD, O ye righteous: for praise is comely for the upright.

34:15: The eyes of the LORD are upon the righteous, and his ears are open unto their cry.

34:17: The righteous cry, and the LORD heareth, and delivereth them out of all their troubles.
Paul is a deliverer - spiritually as well as a 'warning' about the 'next step' in your life.

34:19: Many are the afflictions of the righteous: but the LORD delivereth him out of them all.

37:16: A little that a righteous man hath is better than the riches of many wicked.

37:21: The wicked borroweth, and payeth not again: but the righteous sheweth mercy, and giveth.

37:25: I have been young, and now am old; yet have I not seen the righteous forsaken, nor his seed begging bread.

37:29: The righteous shall inherit the land, and dwell therein for ever.
Remember New Jerusalem...

37:30: The mouth of the righteous speaketh wisdom, and his tongue talketh of judgment.

37:32: The wicked watcheth the righteous, and seeketh to slay him.
Jeremiah 20:10 / II Corinthians 12:15 / Galatians 4:16

55:22: Cast thy burden upon the LORD, and he shall sustain thee: he shall never suffer the righteous to be moved.
Philippians 4:6,7

58:10: The righteous shall rejoice when he seeth the vengeance: he shall wash his feet in the blood of the wicked.
II Thessalonians 1:7-10 / Psalm 149:5-9 / Revelation 19

64:10: The righteous shall be glad in the LORD, and shall trust in him; and all the upright in heart shall glory.

68:3: But let the righteous be glad; let them rejoice before God: yea, let them exceedingly rejoice.

94:21: They gather themselves together against the soul of the righteous, and condemn the innocent blood.

97:11: Light is sown for the righteous, and gladness for the upright in heart.
Psalm 119:105 / 130

97:12: Rejoice in the LORD, ye righteous; and give thanks at the remembrance of his holiness.

118:15: The voice of rejoicing and salvation is in the tabernacles of the righteous: the right hand of the LORD doeth valiantly.

118:19,20: Open to me the gates of righteousness: I will go into them, and I will praise the LORD: This gate of the LORD, into which the righteous shall enter.

146:8: The LORD openeth the eyes of the blind: the LORD raiseth them that are bowed down: the LORD loveth the righteous:

10:11: The mouth of a righteous man is a well of life: but violence covereth the mouth of the wicked.

10:21: The lips of the righteous feed many: but fools die for want of wisdom.

10:28: The hope of the righteous shall be gladness: but the expectation of the wicked shall perish.

10:32: The lips of the righteous know what is acceptable: but the mouth of the wicked speaketh frowardness.

11:8: The righteous is delivered out of trouble, and the wicked cometh in his stead.

11:23: The desire of the righteous is only good: but the expectation of the wicked is wrath.

12:5: The thoughts of the righteous are right: but the counsels of the wicked are deceit.

12:10: A righteous man regardeth the life of his beast: but the tender mercies of the wicked are cruel.

13:5: A righteous man hateth lying: but a wicked man is loathsome, and cometh to shame.

13:9: The light of the righteous rejoiceth: but the lamp of the wicked shall be put out.

13:21: Evil pursueth sinners: but to the righteous good shall be repayed.

13:25: The righteous eateth to the satisfying of his soul: but the belly of the wicked shall want.

14:32: The wicked is driven away in his wickedness: but the righteous hath hope in his death.

15:6: In the house of the righteous is much treasure: but in the revenues of the wicked is trouble.

15:28: The heart of the righteous studieth to answer: but the mouth of the wicked poureth out evil things.

15:29: The LORD is far from the wicked: but he heareth the prayer of the righteous.

18:10: The name of the LORD is a strong tower: the righteous runneth into it, and is safe.

28:1: The wicked flee when no man pursueth: but the righteous are bold as a lion.

28:10: Whoso causeth the righteous to go astray in an evil way, he shall fall himself into his own pit: but the upright shall have good things in possession.

29:2: When the righteous are in authority, the people rejoice: but when the wicked beareth rule, the people mourn.

29:7: The righteous considereth the cause of the poor: but the wicked regardeth not to know it.

29:16: When the wicked are multiplied, transgression increaseth: but the righteous shall see their fall.

How important is it?  Revelation 19:7,8  Let us be glad and rejoice, and give honour to him: for the marriage of the Lamb is come, and his wife hath made herself ready.  And to her was granted that she should be arrayed in fine linen, clean and white: for the fine linen is the righteousness of saints.