The first-round pick signed a three-year, entry-level contract worth $1.075 million annually, the Jets announced on Monday.
Bjorck, 18, went eighth overall to Winnipeg in last month’s draft.
The five-foot-nine centre helped Sweden win gold at the world junior championship last season (three goals, six assists in seven games) and also played for the country at the men’s world championship (one goal, five assists in eight games).
Bjorck also registered six goals and nine assists in 42 games for Djurgårdens in Sweden’s top men’s league.
The Jets have had a relatively quiet off-season, with key signings including defenceman Mario Ferraro (three years, $12 million) and goalie Stuart Skinner (two years, $7.5 million).