Thompson, a center, was a sixth-round pick (No. 183) by the Boston Bruins in the 2003 NHL Draft.

Thompson began his major junior hockey career with Seattle of the Western Hockey League in 2001-02. He was drafted by the Bruins after his second season but remained with Seattle for two more seasons. He joined Providence of the American Hockey League for the 2005 Calder Cup Playoffs.

After signing an entry-level contract with Boston on July 28, 2005, Thompson spent the next three seasons with the Bruins organization before he was claimed off waivers by the New York Islanders on Oct. 8, 2008. He scored his first NHL goal against the New York Rangers on Nov. 4, 2008 and spent two seasons with the Islanders before being claimed by the Tampa Bay Lightning on Jan. 21, 2010. He signed a four-year contract with Tampa Bay on March 23, 2013.

The following season, Thompson had 16 points (nine goals, seven assists) in 81 games but was traded to the Anaheim Ducks on June 29, 2014.

After three seasons in Anaheim, Thompson signed a two-year contract with the Ottawa Senators on July 1, 2017 and was reunited with coach Guy Boucher, who had coached him with the Lightning. He appeared in 43 games before being traded to the Los Angeles Kings.

Thompson spent two seasons with the Montreal Canadiens before he was traded to the Philadelphia Flyers on Feb. 24, 2020.