The Cheetahs confirmed the move for the former Junior Springbok in their official squad update on Monday.
Thomson, who has been with Glasgow since 2017, has joined on a two-year contract until 2022.
Thomson made 31 appearances for scoring 129 points, including five tries.
With Finn Russell, Adam Hastings and Peter Horne always ahead in the pecking order, Thomson's opportunities were limited. However, he impressed in a number of notable Glasgow victories during the Autumn internationals and the Six Nations period.