Career
Edmonton Oilers
Greene was drafted in the second round, 44th overall, by the Edmonton Oilers in the 2002 National Hockey League Entry Draft. Prior to his professional career, he played for three seasons with the University of North Dakota Fighting Sioux. In 2004-2005, Greene captained the Sioux to the National Collegiate Athletic Association Men"s Ice Hockey Championship game, losing to the University of Denver Pioneers, 4–1.
Due to his talent, Greene was encouraged to leave college hockey after only three seasons to start a professional career.
After a successful training camp with the Oilers prior to the 2005-2006 season, Greene signed a professional contract with Edmonton and was assigned to their American Hockey League (AHL) affiliate in Des Moines, the Iowa Stars. He made his National Hockey League debut with the Oilers on December 30, 2005, against the Nashville Predators, and scored his first National Hockey League point on January 25, 2006, away against he Mighty Ducks of Anaheim, assisting on an Aleš Hemský goal.
Wearing sweater number 32 for the first 13 games of his National Hockey League career, Greene changed to sweater number 2 on February 2, 2006, when the Oilers faced off against the Columbus Blue Jackets. Greene contributed an assist in his team"s playoff run.
Greene scored his first National Hockey League goal on December 15, 2006, against Minnesota Wild netminder Manny Fernandez.
The goal was scored in the third period of the game, evening the score at 1–1. The Oilers would eventually score two more goals, winning 3–1. Greene also received the second star of the game due to his effort.
Los Angeles Kings
Greene and his Oiler teammate Jarret Stoll were traded to the Los Angeles Kings on June 29, 2008, in exchange for Kings defenseman Ľubomír Višňovský.
On October 8, 2008, he was named as an alternate captain of the Kings. Nine days later, on October 17, he signed a five-year contract extension with the Kings.
He scored the final goal of the 2012 Stanley Cup Finals in the Kings" 6–1 Game 6 triumph. Greene married Alyssa Miller in 2013.