Greene, 31, has won the Stanley Cup twice in six seasons with Los Angeles. He had four points (four assists) and was plus-5 in 20 games during the 2014 Stanley Cup Playoffs, which ended with the Kings winning their second championship in three seasons.
Greene, an alternate captain, has played for the Kings since he and Jarret Stoll were acquired in a trade with the Edmonton Oilers in 2008. He had two goals and four assists and was plus-6 in 38 regular-season games in 2013-14; he has 13 goals and 56 assists in 504 career games.
The 6-foot-3, 234-pound defenseman could have become an unrestricted free agent July 1 after completing the final season of his 5-year, $14.75 million contract.