The England international signs an initial two-year contract with the Turf Moor side, joining after regular shot-stopper Nick Pope dislocated his shoulder last month.
The 31-year-old had loan spells at Torino and West Ham over the last two seasons, but has opted for a permanent switch to the Clarets this summer, joining Pope and Tom Heaton as the third Three Lions goalkeeper in Sean Dyche's squad.
Hart will have to compete with Heaton, who is recovering from a calf problem, and Anders Lindegaard for the first-choice goalkeeper spot.
Hart's role at City was reduced with the arrival of Pep Guardiola, but the 75-time international insists he holds nothing but affection for City despite his desire to pursue a permanent move away.
"It's been a fantastic experience, I've grown a lot," Hart told City's website as he bid farewell.
"I came here at 19 and I'm going to leave at 31 so it's been a long time and a lot of things have happened - family, friends and a lot of football!
"I certainly feel a lot of love and appreciation. I've always enjoyed the Man City fans, I came here as a Shrewsbury Town player - a kid from Shrewsbury. It was the pinnacle for me to be at this club before they were challenging for the title, and I was welcomed from day one. I think they saw in me someone who was just going to try his best.
"I wouldn't have been able to do the things I've done if I wasn't embraced or happy - so I'm happy to have given the fans some great memories and hopefully I'll be thought of well."
BREAKING: Burnley Football Club is delighted to announce the signing of England international Joe Hart on an initial two-year deal. More to follow. pic.twitter.com/bkyAuXKlMS— Burnley FC (@BurnleyOfficial) August 7, 2018
City chairman Khaldoon Al Mubarak thanked Hart for his contribution to the reigning Premier League champions.
"His 12 years at the club have seen him produce some remarkable performances and heart-stopping saves that will live in the memory for a long time to come," Al Mubarak said.
"His passion for and commitment to this club, evidenced by a remarkable tally of 348 appearances, means he will rightly be regarded as a City legend in perpetuity.
"I want to personally thank him for everything he has given to us over very many years and he leaves with Sheikh Mansour's and my heartfelt best wishes for the next step in his career.
"He will always be welcome at the club."