Hart played almost 350 games for the reigning Premier League champions, establishing himself as number one for club and country, but fell down the pecking order after Pep Guardiola took the helm at City in 2016.
After two seasons out on loan with Torino and then West Ham, the ‘keeper was keen to put down roots again.
The 31-year-old, who cost Burnley a reported £3.5 million ($4.5million), failed to make the England squad for the World Cup despite playing in all but one of the qualifiers.
“It’s definitely the right time for me to move on,” Hart told Clarets Player. “They (Manchester City) are doing fantastic and I’m very happy for them. They need to go on and do their thing and I need to do mine.
“I feel good. I feel like I’m in the right place and I feel like this is my time to kick on now.”
Hart, who has 75 England caps, faces a battle for the number one spot at Burnley. He will be competing against two fellow England internationals, Nick Pope and Tom Heaton, as well as Anders Lindegaard.
Signing a goalkeeper became imperative for Burnley manager Sean Dyche — Pope is out for an indeterminate amount of time with a dislocated shoulder while Heaton has also been struggling for fitness.
Burnley have a Europa League qualifier looming against Istanbul Basaksehir on Thursday and begin their Premier League campaign against Southampton on Sunday.
City chairman Khaldoon Al Mubarak hailed Hart’s enormous contribution to the success of the Premier League champions since he joined 12 years ago.
“Joe Hart’s contribution to Manchester City cannot be overstated,” Al Mubarak said in a statement on Manchester City’s website.
“His 12 years at the club has seen him produce some remarkable performances and heart-stopping saves that will live in the memory for a long time to come.”
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