The former Kilmarnock striker, a free agent since the January transfer window, turned his back on more lucrative offers from England, Greece and Asia to pledge himself to the Perth club until the summer.
Invincibile said: "We have agreed a short-term deal but who knows what might happen after that.
"I'm delighted to get back into football after coming to an agreement with Killie to quit during January.
"After some great years at Rugby Park I wasn't playing regularly and that wasn't fair on me or the club.
"I spoke to various other clubs and could have got more money elsewhere but I want to be playing right away rather than waiting for the start of a new season."
Now the 31-year-old is eager to help Saints secure a top-six finish. He said: "I can play through the middle or wide so I give the boss options."