Since he injured his foot while playing for Spain, Ferran has not been playing for Manchester City.
The Barcelona forward signed a contract with a 1 billion euro buy out clause.
The forward left Valencia to join City 18 months later.
The clubs have not confirmed how much the deal is worth.
In October, Ansu Fati and Pedri signed contract extensions with Barcelona.
The move was imminent on Thursday and the manager said he was happy for the new player.
The club needs to sell some players to comply with the financial regulations of La Liga, as it was believed that Barcelona would pay a further £8.4m in add-ons for the Spaniard.
Thanks to a recent bank loan, Barcelona are able to fund the deal.
Since joining from Valencia in August 2020, the Spain international has made 43 appearances and scored 16 goals for City.
He started City's first six matches of the season, but was dropped to the bench for the goalless draw against Saints in September, and has not played since due to a foot injury.
"Ferran should be proud of what he has accomplished here at Manchester City," said Txiki Begiristain, City's director of football.
His first season in a new country was a success. He worked hard for the team and scored goals which helped us win trophies. We wish him well at Barcelona and the rest of his career.
City feel they have strong depth in forward positions, with Phil Foden, Jack Grealish, Riyad Mahrez, Gabriel Jesus, and Bernardo Silva all vying for a starting spot.
The financial issues of Barcelona meant they were unable to keep hold of Lionel Messi, and allowed him to return to his hometown.
The former City player was forced to retire from football at the age of 33 due to a heart condition.
Ronald Koeman was fired as manager of the club in October after they had just 15 points from their first 10 games.
He was replaced last month by Xavi, who has won three of his first eight matches in charge, but could not stop Barcelona from exiting the group stage of the competition.
