Jeremiah 23:6, This is the name by which He will be called: “YHWH is our righteousness.”
What does it mean to be righteous? It means to be in a right relationship—a relationship functioning in a reconciled state. This is what it means that Christ justifies us by faith (Romans 5:1). For “justify”—δικαιόω (dikaióō)—comes from its root δικαιοσύνη (dikaiosúnē), righteousness. To justify someone, then, is to “do justice,” or “put in the right.” God has always been in a right relationship with Himself in His three persons; this is why only He is righteousness. Therefore, for any of us to be righteous coram Deo (before God) is to be right with Him. None of us can do this by our strength alone. Therefore, God puts us in the right with Him—He becomes our righteousness, i.e. He gives His righteousness to us—as a free gift by faith in Christ (cf. Romans 3:21-26).
The Lutheran Column 