The 26-year-old right-back, not to be confused with the 18th-century Scottish philosopher of the same, made 36 appearances for the Cherries last season.
“I’m delighted,” Smith told his club’s official website. “I’m settled in the area and get along really well with the lads.
“There is nowhere else I want to be at this moment. Everything is going well for me both on and off the pitch and I’m looking forward to that continuing.”
The south-coast side have had a relatively quiet transfer window so far, signing goalkeeper Asmir Begovic and young defender Nathan Ake from Chelsea, and also recruiting veteran striker Jermain Defoe from relegated Sunderland.