Celina, who was raised in Norway from the age of two before joining City's academy at 16, has signed a four-year contract that promises to keep him at the Liberty Stadium until 2022.
He played four times for the City first team, all in the 2015/16 campaign, and has spent the last two seasons on loan at FC Twente and Ipswich Town. Primarily an attacking midfielder, he scored seven goals in 35 Championship appearances for the Tractor Boys.
Celina has told SwanseaCity.com that he jumped at the chance to join the club, not least because of the reputation that new manager Graham Potter built during his time at Ostersund.
"When I heard that Swansea wanted me, I knew straightaway it would be the best move for me because I know the manager wants to play good football," the player explained.
"There was never any doubt for me. I knew about the club's philosophy before anybody told me about it. I saw what the manager did with Ostersund. I watched the way they played against Arsenal and, when he and the club wanted me, there was no doubt.
"I've been at Manchester City a long time, but it was the right time and decision. I have come to Swansea because I want to play regular football. I don't think there's any better place for me."
Potter himself commented, "He's someone we've known about for a while. He is a central attacking midfielder and we see him as a player who can play in between the lines and in the final third. He's played as a second striker and also out wide."