Terms were not disclosed but the deal will run through the 2020-21 season.
Carlo Ancelotti has Everton in contention for a spot in European competition, with the Toffees sitting in seventh place. They are level with Chelsea and Tottenham Hotspur with 33 points.
King scored 53 goals in 184 matches after joining from Blackburn prior to Bournemouth's first Premier League season in 2015-16.
Bournemouth were relegated last season to the second divsion Championship, where they are currently in sixth place and vying for spot in the promotion playoffs.
King is a Norway international, having scored 17 times in 51 appearances for the national squad.
Bournemouth have signed Southampton's Shane Long on loan to fill King's spot.