The 19-year-old winger, who moved to City from Celta Vigo in 2011, has signed a contract with the Spanish giants until 2017.
He will initially join the Barcelona B team, with his buyout clause set at €12 million. That will rise to €35m if he reaches the club's senior side.
Suarez, who made four appearances for Spain during the recent FIFA Under-20 World Cup, had struggled to break in to the first team at the Etihad Stadium following his progression through Celta's academy.
Despite being named City's Young Player of the Year in 2012, he made only two competitive appearances for the first team.
Suarez could feature in Barcelona B's second game of the season against Lugo on Saturday.
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