The former Red Wings and Maple Leafs goalie is expected to back up Tuukka Rask.
Gustavsson, 30, has appeared in 148 NHL games, posting a 60-55-21 record with a 2.89 goals against average and .901 save percentage. He represented Sweden in the 2014 Olympics and won a silver medal.
Rask played 70 games last season, and the Bruins have said they are hoping to develop a dependable backup to cut the starter's workload.
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