Smith, 31, scored 18 goals and recorded 31 points for the Nashville Predators last season.
Smith said he spoke with Bruins center Patrice Bergeron before making his decision to take Boston's offer.
"The way he spoke about the team and the love he has for his teammates, and the respect I have for him," Smith said, "it definitely meant a lot."
Smith has scored 20 or more goals in five of the past seven seasons.
He had been with Nashville for his entire career, spanning nine seasons, and has 162 goals and 330 points in 661 career games.