The Norway international, who joined the Cherries from Blackburn Rovers in 2015, has scored 50 goals in 170 appearances for the south coast outfit.
King’s contract at Dean Court was set to expire at the end of the season.
It was thought that various Premier League clubs wanted his signature after Bournemouth suffered relegation to the Championship on the final day of the 2019/20 campaign.
Burnley were also believed to be interested in signing the 29-year-old striker this month.
🤝 | We have completed the signing of Joshua King from Bournemouth for a nominal fee until the end of 2020/21.#EFC 🔵
— Everton (@Everton) February 2, 2021