The Righteousness of God

The “Righteousness of God” is an expression that occurs in three senses in scripture; the Kingdom-sense, the Gospel-sense, and the Promise-sense. In all cases, righteousness means “equity of character” and has the thought of consistency. The Righteousness of God is God’s total and absolute consistency in His actions with who He is in His own character
Here is a clearer definition of each case:

The Kingdom-sense 

“Seek ye first the kingdom of God and His righteousness.” (Matt. 6:33)

The Lord is exhorting the disciples to recognize God’s supreme power and authority, and to practically live in consistency with Himself

The Gospel-sense 

“Whom God hath set forth to be a propitiation through faith in his blood, to declare his righteousness for the remission of sins that are past, through the forbearance of God.” (Matt. 6:33)

In Romans we have a righteousness that justifies the sinner through the faith of Christ. See full article on this subject! The gospel sense seems to be the primary sense in which this phrase occurs. 

The Promise-sense

“… Obtaining faith by the righteousness of their God and Savior Jesus Christ.” (2 Peter 1:1)

This is God’s righteousness which causes Him to give what is necessary to fulfill His own promises! In this case, faith to unbelieving Jews. This sense is peculiar to the faithful remnant which God ever has in Israel, to whom pertain the promises.