The striker completed his return to Atletico Madrid on Tuesday, ahead of the two clubs meeting in the Champions League the following day, in a deal worth an initial £48.4million.
Costa was frozen out of the club during the summer, with Antonio Conte informing him via text message that his future lay elsewhere, but leaves with two Premier League winners’ medals.
The Spaniard has thanked the fans and backroom staff for their support during his three years in England and hopes his decision to leave is one that can be understood.
“Some cycles begin while others end,” he wrote on Twitter. “My cycle at Chelsea began three years ago – three remarkable years in all aspects – and I will never forget it.
“Two championship titles, a Community Shield, 120 matches, 59 goals and 24 assists later this cycle has ended. Not the way I would have wanted – far from it – but the best way possible.
“The wonderful fans of such equally admirable club and all team mates, as well as all clinical, administrative and logistics staff will remain forever in my mind and in my heart.
“Will bring them with me with the certainty that I will always be by their side as well, and I’m sure they will understand the reason why this cycle of mine has now ended – because I could not lose faith in myself.
“Thank you Chelsea for everything!”