The 27-year-old was one of 10 players deemed surplus to requirements by manager Chris Hughton, and will link up with the club on July 1 when his current contract expires
The 27-year-old made just one Premier League appearance for the Canaries this season, with a further five coming in cup competitions.
Tierney was a regular in the Norwich side that achieved promotion the season before, but lost his place to loan signing Javier Garrido - who has since joined on a permanent deal.
The full-back was one of 10 players released by Chris Hughton, with striker Simeon Jackson and fellow defender Elliott Ward also among those deemed surplus to requirements.
Tierney will join Dougie Freedman's promotion push at the Reebok Stadium, with Bolton narrowly missing out on a play-off position on the final day of the season.