The signing comes six days after the Kings signed center Anze Kopitar to a seven-year extension through 2015-16.
The 25-year-old Greene is in his first season with the Kings after spending three years with Edmonton and was named one of the Kings' assistant captains earlier this month.
Greene, whose contract would have expired after this season, had one goal and nine assists in 78 games for Edmonton two years ago and one assist in 46 games with the Oilers last season. The 6-foot-3, 233-pounder has one goal and 12 assists in 154 career games and one assist in 18 playoff games.
(Copyright 2008 by The Associated Press. All Rights Reserved.)