The Stanley Cup champions announced the deal Monday for King, a restricted free agent.
King's signing means every player who suited up during the Kings' Stanley Cup run is under contract for next season.
King scored five playoff goals last season for Los Angeles, tied with Calder Trophy finalist Adam Henrique of New Jersey for the most postseason goals among rookies.
King was promoted to Los Angeles on Feb. 10 and immediately earned a regular lineup spot alongside fellow rookie Jordan Nolan. King scored 14 points in 27 regular-season games before Los Angeles' run to its first NHL title.
King turned 23 on July 5. The former fourth-round pick made his NHL debut in November 2010.