Cerci, 27, has signed a three-year deal with the Spanish champions.
"I am very happy to have been welcomed here," he told the club's website. "I hope we can have a successful season. Atletico have given me a great opportunity and I want to prove myself."
Cerci, who has won 13 caps for Italy and was part of the Azzurri's World Cup squad this summer, has recorded 21 goals and 19 assists for Torino in the last two seasons and Atletico sporting director Jose Luis Perez Caminero feels he will be a vital addition to the Rojiblancos.
"The agreement reached with Torino for the transfer of Cerci is a joy for everyone. It was a clear objective to finish strengthening our squad ahead of all the challenges that we have in front us this season," he said.
"We've had to make a big effort after all the operations we've made this summer, but we're convinced it's worth the effort because we consider him a key piece for our team.
"He will contribute speed, goals...He's going to give us more alternatives in our attacking play."
Atletico have undergone a summer of change since winning their first Primera Division title since 1996 last season and also reaching the Champions League final.
The likes of Diego Costa, Thibaut Courtois, Filipe Luis and David Villa have left the club, with Antoine Griezmann, Mario Mandzukic, Raul Jimenez, Jan Oblak and Guilherme Siqueira among those brought in by coach Diego Simeone.