The goalkeeper has become the club’s second summer signing after the club agreed a fee of around £10million with relegated Burnley.
Pope has made eight senior appearances for England, and hopes to make Gareth Southgate’s squad for the 2022 World Cup in Qatar later this year.
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"Now I'm here, I can't wait to get started,” said the 30-year-old. “The deal has taken a couple of weeks to come to fruition, but it got over the line really quickly, and I'm delighted to be here, and I'm really looking forward to getting stuck into it."
Head coach Eddie Howe said: "Nick is an exceptional Premier League and international level goalkeeper, so I’m very pleased to be adding strong competition to a very important position.
“There has been a lot of interest in him from other clubs this summer, so I’d like to thank our owners and everyone behind the scenes for getting us ahead of the competition. I’m delighted he is joining us as we prepare for the exciting challenge ahead.”
Pope has spent the past six years at Turf Moor, and helped Burnley qualify for Europe in the 2017/18 season.
"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.”