The England international is thuoght to have agreed a two-year deal with the option for a further year with the 'Clarets'.
The move will give Hart the opportunity to play European football and secure regular game time with both Tom Heaton and Nick Pope currently sidelined with injuries.
Whatsmore, the former Shrewsbury star will line up behind a defence containing fellow England hopefuls Ben Gibson and James Tarkowski, meaning that national team manager Gareth Southgate is likely to be a regular at Turf Moor this season.
Hart is desperate to win back his place in the England squad after missing out on the World Cup in Russia, with a move to Burnley seen as perfect following disappointing loan spells with Torino and West Ham.
The move will end a 12-year City stay for Hart, who is likely to start in goal for Burnley's season opener against Southampton on Sunday.