Edmundson was selected in the second round (No. 46) in 2011 NHL Draft after he had 20 points (two goals, 18 assists) in 71 games for Moose Jaw of the Western Hockey League.

He spent the next two seasons with Moose Jaw and Kamloops of the WHL, getting 48 points (13 goals, 35 assists) in 119 games before signing a three-year, entry-level contract with St. Louis on March 6, 2013.

In 2013-14, Edmundson had eight points (four goals, four assists) and 108 penalty minutes in 64 games for Chicago of the American Hockey League. The following season, he had 12 points (four goals, eight assists) in 30 games for Chicago.

Edmundson made the Blues' opening night roster for the 2015-16 season, making his NHL debut in a 3-1 win against the Edmonton Oilers on Oct. 8, 2015. He scored his first NHL goal in a 4-0 win against the Vancouver Canucks on March 25, 2016 and finished the season with nine points (one goal, eight assists) in 67 games.

Edmundson improved upon his offensive totals the following two seasons, getting 15 points (three goals, 12 assists) in 69 games in 2016-17 and a career-high 17 points (seven goals, 10 assists) in 69 games in 2017-18.

Edmundson had four points (one goal, three assists) in nine games for Canada at the 2018 IIHF World Championship.