The 21st overall pick in the 2005 NHL draft has played two seasons in a Finnish league. Last season, he had a 2.09 goals against average and a .926 save percentage in 30 games with Ilves Tampere.
The 20-year-old was originally drafted by the Toronto Maple Leafs, but the Bruins acquired his rights last year in exchange for goalie Andrew Raycroft.
Rask is travelling to the U.S. to join the Providence Bruins for the AHL playoffs.
"This addition helps to shore up our goaltending situation for the future," Bruins general manager Peter Chiarelli said.
The team did not disclose contract terms and said Rask would not be available to comment until Sunday.