The Norway international enjoyed a fruitful goalscoring spell during the second half of last season, finding the back of the net 12 times in just 14 games before ending the campaign on 16 goals overall.
King's form led to speculation over his future earlier this summer, but he has now put pen to paper on a contract which will keep him at the Vitality Stadium until 2021.
"There was a lot of talk during the summer but I always made it clear I wanted to stay here," King told the club's official website.
"AFC Bournemouth is a great club that is always looking to improve, the manager has been brilliant with me and we have a fantastic squad. The future here is bright and I'm really happy that I will be a part of that."
Chief executive Neill Blake added: "I am delighted that Joshua has committed his long-term future to the club. During the last year he has become a key player here, both with his goals and performances, and was instrumental in the team finishing ninth in the Premier League in 2016-17.
"Joshua is the fifth player we have tied down to a new deal this summer and, combined with our four new signings, we can all be excited about the direction this club is heading in."
King, 25, has failed to find the back of the net in Bournemouth's three outings so far this season.