Morrow comes from a hockey family. His father, Dave Morrow, played for the Indianapolis Racers of the World Hockey Association.

The Pittsburgh Penguins selected Morrow in the first round (No. 23) of the 2011 NHL Draft, but he never played a game for them after signing on Aug. 3, 2011.

He played one more season for Portland of the Western Hockey League, finishing with 64 points (17 goals, 47 assists) in 62 games. Morrow spent most of the 2012-13 season with Wilkes-Barre/Scranton of the American Hockey League before being traded to the Dallas Stars on March 24, 2013.

On July 4, 2013, Morrow was acquired by the Boston Bruins as part of an eight-player trade which sent forward Tyler Seguin to the Stars. Morrow made his NHL debut with the Bruins on Oct. 30, 2014, and scored his first NHL goal against the Penguins on Nov. 24. However, after playing three more games, he was sent to Providence of the AHL for the rest of the season.

Morrow played 33 games for the Bruins in 2015-16 and 17 in 2016-17 before signing with the Montreal Canadiens as a free agent on July 1, 2017. He was having his best offensive season in the NHL (five goals, six assists) in 38 games before being acquired by the Winnipeg Jets on Feb. 26, 2018.

Morrow had five points (one goal, four assists) in 18 games for the Jets. He dressed for six of their 17 games in the Stanley Cup Playoffs, including scoring the winning goal in Game 1 of the Western Conference First Round against the Minnesota Wild.

The Jets signed Morrow to a one-year contract on June 26, 2018.

NOTES & TRANSACTIONS

• WHL West First All-Star Team (2012)
• Traded to Dallas by Pittsburgh with Pittsburgh's 5th round pick (Matej Paulovic) in 2013 NHL Draft for Brenden Morrow and Minnesota's 3rd round pick (previously acquired, Pittsburgh selected Jake Guentzel) in 2013 NHL Draft, March 24, 2013.
• Traded to Boston by Dallas with Loui Eriksson, Reilly Smith and Matt Fraser for Tyler Seguin, Rich Peverley and Ryan Button, July 4, 2013.
• Signed as a free agent by Montreal, July 1, 2017.
• Traded to Winnipeg by Montreal for Winnipeg's 4th round pick in 2018 NHL Draft, February 26, 2018.
• Signed as a free agent by New Jersey, October 6, 2019.