Smith's contract is worth $550,000 at the NHL level and $80,000 in the AHL.
During a conference call Tuesday night, Bruins general manager Peter Chiarelli said he was looking to add another goaltender to the organization.
Smith, 25, spent the 2013-14 season with the Springfield Falcons, the AHL affiliate of the Columbus Blue Jackets, and finished with a 21-14-3 record, a 2.78 goals-against average and a .898 save percentage.
The Bruins recently signed goaltending prospect Niklas Svedberg to a one-year, one-way contract worth $600,000. Chiarelli said Svedberg still needs to earn the spot as Tuukka Rask's backup, and Smith's presence will help create that internal competition among Svedberg, Smith and Malcolm Subban.
Smith, who also spent time in the Nashville Predators system with the Milwaukee Admirals, has an overall AHL record of 87-60-10, a 2.48 GAA and a .912 save percentage, including nine shutouts in 166 games.
Chiarelli said he wouldn't go full force into the free-agent period, and in the first two days on the open market, the Bruins have signed Smith and defenseman Christopher Breen.
Breen, 25, signed a one-year, two-way contract Tuesday worth $600,000 at the NHL level and $175,000 for the AHL. Breen made his NHL debut with the Calgary Flames last season but has spent five seasons in the AHL with the Abbotsford Heat. The 6-foot-7, 224-pounder played 245 games and accumulated 172 penalty minutes in the AHL.