The Spain international has already passed a medical at Stamford Bridge, with the Blues having agreed to sign the striker for £35m.
And club president Cerezo admits that, despite attempting to convince Costa to stay, Atletico can do nothing to keep him.
"We've always tried to convince our players to stay, but the difference between our finances and that of other clubs is very large," he told Sky Sports.
Cerezo also appeared to confirm Belgium goalkeeper Thibaut Courtois would return to Chelsea after three seasons on loan at Atleti.
"Chelsea can count on Courtois, because he is their player," he added.