The contract has an annual cap hit of $1.275 million, the team said.
Kuraly scored six goals last season, his first full season in the NHL. He had two goals and a pair of assists in the playoffs.
Also Tuesday, the Bruins signed forward Anton Bildh to a two-way contract that would pay him $650,000 in the NHL. He had 11 goals and 15 assists with Providence of the AHL last season.
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