Prior to his professional career, he played for three seasons with the North Dakota Fighting Sioux men's ice hockey team.

In 2004–05, Greene captained The Fighting Sioux to the NCAA Men's Ice Hockey Championship game, losing to the University of Denver Pioneers, 4–1.

[citation needed] 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 2005–06 season, Greene signed a professional contract with Edmonton and was assigned to their American Hockey League (AHL) affiliate in Des Moines, the Iowa Stars.

[citation needed] Greene scored his first NHL goal on December 15, 2006, against Minnesota Wild netminder Manny Fernandez.

[citation needed] On June 30, 2016, Greene was placed on unconditional waivers by the Kings for the purpose of buying out the final two years of his contract, following a season where the defenseman played only three games due to a shoulder injury, picking up no points and eight penalty minutes.