On the surface, this would seem to be a ridiculous thing to say..how could God not be righteous?

Righteous is defined as "moral perfection".                                                                   

How could a perfect God not be righteous?                                                                   

And yet, this "righteousness" of God is the very foundation upon which our faith, that of Paul's followers, "believers", is based.

Concordanr Publishers (the originators of the Concordant Bible), in their recent "Unsearchable Riches" pamphlet *..published quarterly, make this point very clear that this is what Paul is saying.

He is not saying that righteousness is from God, though this is true. It is that righteousness from God that brings justification to all.."the evangel itself makes it evident that God is righteous in this work of justification..which leads finally to all being constituted righteous."

It is God's own righteousness that is being adressed.  "God's evangel is a message concerning God's Son, and is a message of God's power for SALVATION, and in it God's own righteousness is revealed."

This may be a little deep, even esoteric, but consider "the insight into God's righteousness which the evangel provides is a guard against much wrong thinking about God and His salvation."

In short, this makes it clear that our salvation is due solely to the grace of God, and no amount of work on our part can affect if whatsoever, as so many believe..paulnbob

*I suggest you subscribe to this for increased knowledge of Paul's teaching.