The Scotland international stand-off makes the switch after four seasons with the club, having made his debut in January 2021 in an 1872 Cup clash with his new team at Scottish Gas Murrayfield.
Thompson has scored 287 points in his 47 appearances for the Warriors to date, as well as taking home the McCrea Financial Services Player of the Season and Land Rover Young Player of the Season awards at the end of the 2020/21 campaign.
The former Glasgow Hawk and Ayrshire Bull made his Scotland debut off the bench against Tonga in October 2021, having also previously represented his country at U20 level.
Speaking following the move, Thompson said: "I'm very grateful to Glasgow Warriors for the opportunities that I've had which have allowed me to develop as a player and I've really enjoyed my time at the club."