He has played in the National Hockey League (NHL) for the New Jersey Devils, Vancouver Canucks, Anaheim Ducks, Dallas Stars, Washington Capitals, Calgary Flames and Chicago Blackhawks.

Morrison was selected 39th overall in the 1993 NHL Entry Draft by the Devils after a season in the British Columbia Junior Hockey League (BCJHL); he had won rookie of the year honours for the Interior Conference as a member of the Penticton Panthers.

Turning professional in 1997–98, Morrison was named to the American Hockey League (AHL) All-Rookie Team as a member of the Albany River Rats.

As a member of the team's "West Coast Express" line (alongside Markus Näslund and Todd Bertuzzi), Morrison enjoyed the most successful years of his career, posting three consecutive 60-point seasons.

Morrison played one season with the Penticton Panthers of the British Columbia Junior Hockey League (BCJHL) in 1992–93, recording 94 points (35 goals and 59 assists) over 56 games.

He ranked second in team scoring, behind Marcel Sakáč,[1] and was awarded the Bruce Allison Memorial Trophy as the Interior Conference's rookie of the year.

Playing in his sophomore year (1994–95), Morrison improved to 76 points (23 goals and 43 assists) over 39 games and received his first of three consecutive CCHA First Team All-Star selections.

[6] Michigan's championship-winning team that year included five future NHL players—Morrison, Botterill, Blake Sloan, John Madden, Marty Turco and Bill Muckalt.

[8] He was seen as an unlikely candidate to secure a roster spot with the Devils; ahead of Morrison on the depth chart were numerous centres, including Doug Gilmour, Bobby Holík and Petr Sýkora.

[10] He finished second among League rookies in scoring, eight points behind Daniel Brière of the Springfield Falcons,[10] and was named to the AHL All-Rookie Team.

[4] His AHL season included a five-goal game against the Hartford Wolfpack on April 1, 1998; two of his goals came short handed into an empty net, as part of a 5–2 Albany win.

He was called up to the Devils in December 1997 as a replacement for winger John MacLean, who had been informally suspended by General Manager Lou Lamoriello after requesting to be traded.

With Doug Gilmour having left the team as a free agent in the 1998 off-season, Morrison was expected to help fill the void at centre.

[15] He ranked fifth in Calder Memorial Trophy voting as the League's rookie of the year with one first-place ballot (the award was given to the Avalanche's Chris Drury).

[17] While overseas, Morrison and Eliáš played for Czech teams SK Horácká Slavia Třebíč and HC Pardubice as they waited for contract negotiations to resume.

[18] After recording 26 points over 44 games with the Devils, Morrison was traded to the Vancouver Canucks on March 14, 2000, alongside centre Denis Pederson, in exchange for winger Alexander Mogilny.

[23][24][25][26] During a game on January 9, 2002, Morrison replaced Andrew Cassels as the centreman on the team's first line with wingers Markus Näslund and Todd Bertuzzi.

[22] In 2003–04, Morrison registered 22 goals and 60 points over 82 games as all members of the Canucks' top line experienced declines in offensive production.

Having skated from the corner boards with the puck, Morrison stickhandled across the net and scored past Calgary goaltender Miikka Kiprusoff.

[37] In lieu of the 2004–05 NHL lockout, Morrison went overseas to play in the Swedish Elite League, signing with Linköpings HC on September 15, 2004.

[21] Head Coach Marc Crawford recalled that by the end of the season, the line of Morrison, Bertuzzi and Näslund had been surpassed as the top unit by Daniel and Henrik Sedin.

[43] Later in the campaign, he set a Canucks record for consecutive regular season games played (colloquially known as an "ironman streak"); he had not missed a contest since arriving to the team from New Jersey.

[43] Three days later, he became the League's active ironman when Avalanche defenceman Kārlis Skrastiņš was forced to miss a game with a knee injury.

[22] The following month, Morrison tore the ACL in his right knee during a game on March 28, forcing him to miss the remaining four contests of the regular season.

[21] Becoming an unrestricted free agent in the off-season, Morrison ended his career with the Canucks ninth overall on the team's all-time scoring list with 393 points in 543 games.

[52] He had received interest from as many as nine NHL teams, including the Canucks, who offered a one-year, US$1.9 million deal prior to Morrison's free agency.

At the time of the injury, Morrison was leading the Flames with a plus-minus rating of +13 while centring the team's top line with Jarome Iginla and Alex Tanguay.

[70] Four years later, Morrison was selected again to the Canadian team for the 2004 IIHF World Championship in Prague and Ostrava, Czech Republic.

He was a late addition, replacing Mario Lemieux, who chose not to attend due to commitments with his club team, the Pittsburgh Penguins.

Since retirement, he has ventured into business with Geoff Sanderson establishing a company called Breakaway Matting Inc.[82] He currently hosts a fishing and adventure show, Reel West Coast, on CHEK TV-DT[83] and YouTube.