Cerci completed a full training session with Milan for the first time on Saturday after passing his medical on Friday, and the 27-year-old admitted he was relieved to get the deal finalised as he looks to rebuild his career.
The winger barely played in six months with Atletico, coming off the bench six times in La Liga, and wants to return to the type of form that saw him score 13 goals in 37 Serie A matches for Torino.
Cerci has joined Milan as part of the deal that has seen Fernando Torres head to the Vicente Calderon on loan for the rest of the season.
"It's taken a little longer but I'm now happy," Cerci told Milan's website.
The Italy international's first chance to make his Milan debut will be against Sassuolo at the San Siro on Tuesday.
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