The 27-year-old Italy international passed a medical on Friday and has now sealed a switch to San Siro, reportedly for 18 months, after failing to make an impact with the Spanish champions.
Cerci joined Diego Simeone's side from Torino in August, but has made only nine appearances in all competitions.
The former Fiorentina man moves to Milan as part of the deal which took Fernando Torres back to his boyhood club.
Cerci trained with his new team-mates over the weekend and it is not clear if he was signed in time to feature in Tuesday's Serie A clash with Sassuolo.
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