The Spanish champions announced on Sunday that they had reached an agreement with the Serie A side to take Cerci to the Vicente Calderon on a three-year-deal.
And the former Fiorentina and Roma man has now finalised the details of his transfer to Atletico, making him their eighth signing of the transfer window.
Cerci's move to the Spanish capital strengthens an Atletico attack that has undergone a rebuild following the departure of last season's top scorer Diego Costa to Chelsea.
Centre forwards Mario Mandzukic and Raul Jimenez have already arrived in the transfer window, while Antoine Griezmann was brought in to provide a creative threat from the left-wing.
The 27-year-old Cerci, who is thought to have cost €16million (£12.6m), scored 13 goals in 37 Serie A appearances last term and was part of Italy's squad at the World Cup.