The 26-year-old midfielder is the Serie A leader's first signing of the January transfer window and will reportedly cost an additional €9.5 million ($15.3 million) to sign permanently at the end of the campaign.
Meite makes the switch to Milan with two and a half years of Serie A experience behind him, having arrived at Torino from Monaco in July 2018.
He made 82 league appearances for Torino, including 11 starts this season.
Milan announced the loan capture on its website on Saturday (AEDT), with Meite to wear the number 18 jersey.
The former France Under 20 international has also previously represented Auxerre, Lille and Bordeaux.