The former Barca midfielder has been heavily linked with taking over at Camp Nou in the close-season, having been at Celta since June last year.
With Celta able to finish as high as eighth in the Spanish top flight, the 44-year-old confirmed on Friday he will leave the Estadio de Balaidos.
Luis Enrique previously managed at Roma and Barcelona B, with his exit likely to intensify rumours he will be named as Gerardo Martino's replacement at Barca.
He paid tribute to his Celta squad but stated he did not know where he would coach next season.
"I want to pay special tribute to the players, the best group of people I've had as a coach," he said.
"I've tried to repay Celta for the faith they put in me with many hours of hard work, effort and finally, with results
"I have a lot of affection for Vigo. They have treated us greatly here, but there are other things. For example, living away from family is hard.
"Believe it or not, but right now, I don't know which team I will be coaching next season."
