London - City manager Pep Guardiola's move for Bravo is likely to mean England goalkeeper Hart will be sold before next week's transfer deadline after he lost his place to back-up Willy Caballero at the start of the season.
Guardiola, who arrived from Bayern Munich in the close season, wanted to sign Bravo because he felt Hart's passing wasn't good enough to fulfil his desire for a 'sweeper-keeper' who can effectively retain possession.
Chile international Bravo has signed a four-year contract and is reported to have cost City around 17 million ($22 million, 19 million euros).
Caballero surprisingly started City's first three games of the season ahead of Hart, whose appearance against Steaua Bucharest in the Champions League on Wednesday may well prove to be his last in a City shirt after 10 years with the club.
While Guardiola is respectful of Hart's qualities, he believes Bravo's wealth of experience and his leadership will prove invaluable as the Spanish coach looks to put his mark on the City squad in his first season in English football.
"Claudio is a fantastic goalkeeper and an excellent addition to our squad," Guardiola told City's website.
"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 made 75 appearances for Barcelona since joining from Real Sociedad in 2014.
The 33-year-old won eight trophies including back-to-back La Liga titles, and was named in the 2014-15 La Liga team of the season.
Bravo is Chile's most capped player on 106 international appearances and was voted goalkeeper of the tournament after captaining his country to Copa America glory earlier this year.
Bravo hopes to add to his trophy collection with City and admitted the chance to play for Guardiola was too good to turn down.
"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," Bravo said.
"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."