The youngster decides to leave the Premier League runners-up, with whom he struggled to break into the first team, for a return to his home country after two years abroad
The 19-year-old had long been linked with a return to Spain and has now signed a four-year deal with the Blaugrana, where he will start in the club's B team.
Suarez's buy-out clause has been set at €12 million (£10.3m) and will rise to €35m (£30m) once he gets promoted to Barcelona's first team.
The attacking midfielder, who has been capped at Under-20s level for Spain, came through the ranks of the Celta Vigo youth academy but left his boyhood club for City in the summer of 2011.
However, Suarez failed to break into the first team, despite being voted the club's Young Player of the Season in 2012, and has opted to move on.