The righteousness of God, is all that God demands and approves, to be in good standing with him, and is ultimately found in Christ. By faith in Jesus Christ, the righteousness of Christ was imputed unto us.

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ROMANS 3:21-22   But now the righteousness of God apart from the law is manifested,
  being witnessed by the prophets.
  Vs.22   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.

ROMANS 3:26   To declare, I say, at this time his righteousness, that he might be just,
  and the justifier of him who believeth in Jesus.

ROMANS 4:3   For what saith the scripture, Abraham believed God, and it was counted
  unto him for righteousness.

ROMANS 4:6   Even as David also decribeth the blessedness of the man unto whom
God imputeth righteousness apart from works.

ROMANS 10:4   For Christ is the end of the law for righteousness to every one that
  believes.

2 CORINTHIANS 5:17   For he hath made him who knew no sin, to be sin for us, that
  we might be made the righteousness of God in him.

PHILIPPIANS 3:9   And be found in him, not having mine own righteousness, which is
  of the law, but that which is through the faith of Christ, the righteousness which is of
  God by faith.

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