A third-round pick (No. 89) by the Blue Jackets at the 2013 NHL Draft, Bjorkstrand scored 144 goals over three seasons for Portland of the Western Hockey League and signed a three-year contract with the Blue Jackets on Dec. 26, 2013.

Two days after his NHL debut, Bjorkstrand scored his first and second NHL goals against the New Jersey Devils on March 19, 2016. After the Blue Jackets finished their season, Bjorkstrand was sent to Lake Erie of the American Hockey League and scored in overtime of Game 4 to complete a sweep of Hershey in the Calder Cup Finals. He was named the most valuable player of the AHL playoffs with 16 points (10 goals, six assists) in 17 games.

Bjorkstrand scored 40 points (11 goals, 29 assists) in 2017-18, his first full NHL season. He had three points (one goal, two assists) in the Blue Jackets' six-game loss to the Washington Capitals in the Eastern Conference First Round.

He scored an NHL career high 23 goals in 2018-19, then helped Columbus win a Stanley Cup Playoff series for the first time with a sweep against the Tampa Bay Lightning. Bjorkstrand finished with two goals and three assists in 10 playoff games.

Despite scoring 57 points (28 goals, 29 assists) for the Blue Jackets in 2021-22, Bjorkstrand was traded to the Seattle Kraken on July 22, 2022, for a third- and fourth-round pick in the 2023 NHL Draft. He and Daniel Sprong combined for two goals in 10 seconds of the second period in a 6-5 shootout loss to the Vancouver Canucks on Dec. 22. In Game 7 of the 2023 Western Conference First Round, Bjorkstrand scored twice to help the Kraken win its first-ever playoff series and eliminate the defending Stanley Cup champion Colorado Avalanche with a 2-1 victory.

Bjorkstrand was acquired by the Tampa Bay Lightning in a three-team trade with the Seattle Kraken and Detroit Red Wings on March 5, 2025. He was named to Team Denmark's roster for the Olympic Winter Games Milano Cortina 2026.