The Algerian defender has completed a move to San Siro as Massimiliano Allegri seeks to increase his options at full-back with Taiwo failing to impress this term
The Stadio Via del Mare outfit have not released any information about the transfer fee or the length of Mesbah's contract with the San Siro outfit, but revealed that they have secured the services of Milan youngster David Speziale on a co-ownership deal, starting in the summer.
Mesbah, 27, joined Lecce from Swiss side FC Luzern in 2009 and has been an ever-present figure in the Serie A club's rearguard since.
The arrival of the Algeria international will strengthen suggestions that Taye Taiwo could be on his way out of the club in January.
The Nigeria international has voiced his unhappiness with his situation, having made just eight appearances since joining the club from Marseille in the summer.
Meanwhile, Lecce have announced that loanee Rodney Strasser has been allowed to return to Milan after suffering an injury which will rule him out for the rest of the campaign.