The Chile international, 33, has put pen to paper on a four-year deal at the Etihad Stadium, with reports suggesting he has moved for a fee of around £17million.
Bravo's arrival at City is widely expected to lead to the departure of Joe Hart, the England goalkeeper who has been with the club for 10 years and made his first appearance of the season on Wednesday.
Bravo is set to become number one at City under their ex-Barca boss Pep Guardiola, with Willy Caballero as back-up.
Caballero started the Blues' first three games of the season ahead of Hart, whose subsequent run-out against Steaua Bucharest on Wednesday may well prove to have been a farewell appearance.
Bravo said on City's official website on Thursday: "I'm very proud to be joining Manchester City
I know the club is building something very special and I hope I can be part of many successes in the coming years.
"I have followed City's progress in recent years and obviously know some of my new team-mates from the Copa America.
"It is not easy to leave a club like Barcelona where I had two fantastic years, but the opportunity to work with Pep Guardiola was too good to refuse.
"Now I will challenge the other great goalkeepers the club has and together I hope we can win many trophies."
Guardiola said: "Claudio is a fantastic goalkeeper and an excellent addition to our squad.
"He has experience and great leadership qualities and is in the prime of his life
He is a goalkeeper I have admired for a number of years and I'm really happy he is now a City player."
Bravo has had a trophy-laden couple of years since joining Barca from Real Sociedad in the summer of 2014.
Being used by the Catalan club in LaLiga games - 70 in total - and virtually no other competitions, he has helped them secure the title in each of the last two seasons.
Bravo, Chile's most capped player on 106, also captained Chile to Copa America glory both last summer and this.
Source : PA
Source: PA