"Our coaching staff has been an integral part of the success of our team the last three years," general manager Dean Lombardi said in a statement. "We are extremely pleased that they will remain part of our team and continue together as we strive for excellence."
Stevens and Ranford were part of the Kings' Stanley Cup-winning teams in 2012 and 2014. Payne joined the Kings in July 2012 and was part of this year's championship team.
Stevens, 48, has been with the Kings for four seasons as an assistant coach, under Terry Murray then Darryl Sutter. Stevens served as interim coach for four days between Murray and Sutter's tenure in 2011-12.
The former NHL defenseman has played a major role in the development of several of the Kings' young defensemen. Los Angeles has been among the NHL's stingiest defenses during his tenure, and the Kings won the William Jennings Trophy this season by allowing the fewest goals during the regular season.
Payne, 43, oversees the offense, which led the NHL in playoff scoring with an average of 3.38 goals per game and ranked sixth in playoff power-play percentage at 23.5 percent.
Ranford, 47, has spent the past eight seasons with the Kings after a 15-year playing career that included the Conn Smythe Trophy as MVP of the 1990 Stanley Cup Playoffs, when he led the Edmonton Oilers to their fifth championship in seven years. He also was a member of the Oilers' Cup-winning team in 1988. Ranford has been instrumental in the development of Kings' goalies at all levels of the organization. Los Angeles goaltenders led the NHL with 13 regular-season shutouts and allowed a League-low 168 non-shootout goals.