Diego Costa and Atletico Madrid have terminated their contract by mutual consent.
Costa will be free to join a new club on a free transfer.
Diego Simeone said Costa had given "everything" to the club.
"He has given us a lot and we have given him a lot," Simeone told a news conference on Tuesday.
"He needs new challenges because he feels good, strong, in good form. I can only imagine that wherever he goes he will do well because he is a fighter.
"Diego has always given us everything, in a sporting and human sense. Let's hope he finds the right path and we can see each other again and give each other a hug."
Costa rejoined Atleti in January 2018 for €66 million after three-plus season with Chelsea.