Wright began his major junior career with the Vancouver Giants in 2005–06, debuting in two WHL games. The following season, he recorded 12 points in 48 games during his WHL rookie season. He helped the Giants finish as league runner-up in the playoffs to the Medicine Hat Tigers before winning the 2007 Memorial Cup championship against the same Tigers squad in the CHL title final. In 2007–08, Wright improved to 36 points and was drafted 117th overall by the Tampa Bay Lightning in the 2008 NHL Entry Draft. Upon being drafted, Wright continued to play for the Giants, scoring 21 goals and 47 points in 2008–09.
Wright made the Lightning roster for the start of the 2009–10 season, making his NHL debut on October 3, 2009, in a 6–3 loss to the Atlanta Thrashers. He played the game opposite former Giants linemate Evander Kane of the Thrashers, who was also playing his first NHL game. Wright scored his first NHL goal in his seventh game on October 22, 2009, against Evgeni Nabokov of the San Jose Sharks.
After scoring two goals and three assists through 48 games, he was sent back to the Giants on January 21, 2010. Returning to the WHL, he notched six goals and 19 points through the final 21 games of the 2009–10 WHL season. In the playoffs, the Giants advanced to the semifinals, where they were eliminated in six games by the Tri-City Americans. Wright recorded seven goals and 16 points in 16 post-season games.
Wright began the 2010-11 season in the AHL. He played 15 games for the Lightning's top affiliate, the Norfolk Admirals, before making his 2010–11 NHL season debut for Tampa Bay in an away game against the Philadelphia Flyers on November 18, 2010. On December 2, 2011, Wright was traded by the Lightning, along with Mike Vernace, to the Florida Panthers for Mike Kostka and Evan Oberg. He was then immediately assigned to AHL affiliate, the San Antonio Rampage. On January 18, 2013, the eve of the 2012–13 season, Wright was claimed off waivers from the Panthers by the Winnipeg Jets.
After two seasons with the Jets, Wright was released as a free agent, and with limited interest around the league, signed his first contract abroad with Croatian club KHL Medveščak Zagreb of the Kontinental Hockey League, on September 15, 2014.
On July 2, 2015, Wright returned to North America, signing a one-year, two-way contract with the New York Islanders. He was assigned to AHL affiliate, the Bridgeport Sound Tigers for the duration of the 2015–16 season.
In the following off-season, having been unable to add to his NHL resume, Wright returned to the KHL, signing a one-year deal with Russian club, Admiral Vladivostok on September 8, 2016.
Wright is the grandson of former Saskatoon mayor Cliff Wright. The elder Wright served as the city's mayor from 1976 to 1988 and was instrumental in the construction of Saskatchewan Place, which opened at the end of his term in 1988.