The 30-year-old leaves for an undisclosed fee, believed to be £12m.
Pope was expected to stay in the Premier League in a World Cup year, after the Clarets’ relegation in May, and had been linked with a string of clubs over the summer, including West Ham and promoted duo Fulham and Nottingham Forest.
A club statement said: “The club would like to thank Nick for all his efforts during his time at Turf Moor and wish him all the best for the future.”
Pope joined Burnley six years ago as the Clarets prepared for life back in the Premier League after winning the Championship, ironically sealing the title with a 3-0 win at the Valley with Pope in opposition.
After spending his first season developing under Tom Heaton and then Paul Robinson, he came in for the injured Heaton in September 2017, and played the rest of that season as Burnley finished seventh and qualified for the Europa League.
He also earned his first England cap against Costa Rica at Leeds and went to Russia 2018 as part of Gareth Southgate’s squad.
Like Heaton, Pope then dislocated his shoulder early in the Europa League qualifier first leg at Aberdeen, returning in the FA Cup in January, but not making a Premier League appearance that season.
Heaton was sold to Aston Villa in August 2019, after Pope signed a new contract to 2023, and Pope has only missed eight Premier League games in the following three seasons, with a knee problem keeping him out of Euro 2020 last summer.
Pope has made 155 appearances for the club.
Vincent Kompany would still have Wayne Hennessey and Bailey Peacock-Farrell, Wales and Northern Ireland number ones respectively, at his disposal, while he has also been linked with Manchester City’s 23-year-old Kosovan keeper Arijanet Muric, who spent last season on loan in Turkey at Adana Demirspor.
And Kompany is thought to want his new side to build up from the back, requiring central defenders and a goalkeeper with good feet – with Pope’s distribution his only real weak point.