The 27-year-old Valencia defender rejected the chance to join Napoli in favor of the Rossoneri, according to his agent.
The 27-year-old Rami's future at the Mestalla has been the subject of speculation recently, as the France international was slapped with a one-week suspension without pay for publicly criticizing coach Miroslav Djukic and teammates.
Bronzetti has confirmed that he has sealed an escape route for the defender, who snubbed interest from Napoli prior to agreeing to join the Rossoneri early in 2014.
"I have just concluded the transfer, so it is complete," Bronzetti told Radio Kiss Kiss. "The player will go to Milan despite recent interest from Rafa Benitez at Napoli. He [Rami] was wanted by many clubs, but he chose the Rossoneri."
Reports emanating from Italy have suggested that a fee of 400,000 euros will be paid by Milan for the loan, while a further 7 million will be required at the end of the season should the Italian giant wish to make the move permanent.
Rami, whose contract with Los Che runs until 2015, joined Valencia from Lille in 2011 and has subsequently made 93 appearances for the club.