Brazilian shot-stopper Gabriel has moved in the opposite direction on a loan deal for the remainder of the 2016-17 campaign after agreeing a new deal with the Rossoneri until 2019.
The 40-year-old Storari previously enjoyed a spell with Milan between January 2007 and June 2010, making 13 appearances in all competitions.
He eventually left Milan for Juventus, where he served as understudy to Gianluigi Buffon until leaving for Cagliari in 2015.
Storari helped Cagliari win promotion back to Serie A in 2015-16 and remained a key figure in the opening stages of this term, but lost his starting berth late in 2016.
Storari will be serving as back-up goalkeeper to the 17-year-old Gianluigi Donnarumma at San Siro.