Terms were not announced, but the deal is reportedly worth $2.5 million annually.
Bjorkstrand, 23, will again be a restricted free agent when his deal is up in 2021.
He finished with 11 goals and 29 assists in 82 games with Columbus last season.
"Oliver is a gifted player with a tremendous shot and scoring instincts who has improved steadily during his first three season. as a pro," said general manager Jarmo Kekalainen. "He is just scratching the surface of the type of player he can be and we believe he has the potential to be a dynamic offensive player for our club."
A third-round pick by the Blue Jackets in the 2013 NHL Draft, Bjorkstrand starred for the American Hockey League's Lake Erie/Cleveland Monsters before earning a full-time role with the NHL club last season.
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