The 30-year-old had been out of contract at Kenilworth Road this summer, but although the club announced they were in negotiations with the popular Scot, he has opted to move to Ashton Gate instead.
Naismith leaves after a terrific season with the Hatters, playing 45 matches and scoring three goals, including a fantastic last-minute winner against Bournemouth back in January.
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He also contributed eight assists too, voted Players’ Player of the Season, and Player of the Season, named in the EA Sports FIFA 22 EFL Team of the Season as well.
The ex-Portsmouth and Rangers player departs Town having made 68 appearances in total after arriving on a free transfer in January 2021, following his exit from Wigan Athletic.