The Sky Bet Championship club confirmed the deal on Tuesday afternoon, with the 21-year-old agreeing a four-year deal at the Liberty Stadium.
Celina started his career at Norwegian outfit Stromsgodset before joining City’s academy.
He made four first-team appearances during the 2015/16 campaign, including once in the Premier League.
A loan spell at FC Twente followed before Celina spent last year at Ipswich, scoring eight goals in 38 appearances for the Tractor Boys.
“When I heard that Swansea wanted me, I knew straight away it would be the best move for me because I know the manager wants to play good football,” Celina said in an interview.
“There was never any doubt for me. I knew about the club’s philosophy before anybody told me about it.”
Celina’s arrival came on the same day Swansea signed Barrie McKay from Nottingham Forest for an undisclosed fee.
The 23-year-old, who can play in a number of attacking positions but is happiest out wide on the left, put pen to paper on a three-year deal.
He trained with Graham Potter’s squad for the first time on Tuesday morning and, like Celina, is in contention to make his debut when the Swans begin their Championship campaign at Sheffield United this weekend.
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