The expense for the 33-year-old Chile global could ascend with £1.7m of additional items, say the Spanish club.
Bravo, who has marked a four-year contract, is required to begin in front of England goalkeeper Joe Hart and Argentine Willy Caballero.
Barca have supplanted Bravo with Netherlands global Jasper Cillessen, who joins from Ajax.
Bravo said: "I'm extremely pleased to join Manchester City.
"I know the club is building something extremely uncommon and I trust I can be a piece of numerous achievements in the coming years."
Bravo joined Barcelona in 2014 and won two La Liga titles and the Fifa Club World Cup.
He was additionally part of the Champions League-winning squad in 2015, yet never played in the opposition for Barca.
"It is difficult to leave a club like Barcelona where I had two fabulous years, yet the chance to work with Pep Guardiola was too great to won't," he included.
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