After Julius Augustus Caesar and the Five Good Emperors. You can argue when it really started, but the fact is that the Roman military was reliant on former legionaries joining mercenary bands to keep the wheels on by the end of the 1st Century AD, and two centuries later, something like a third of the legions were foreign born and serving just to "become Romans". This should sound familiar, if you follow modern military news.

Also, fun historical tidbit. The first person to become a Christian without becoming a Jew first, Cornelius, was a Italian mercenary working for a group that consisted of legionaries that had completed their service and refused to live in Rome.