Loose-head Reid had been on a partnership contract with FOSROC Super6 side Ayrshire Bulls, helping the Millbrae outfit to a place in the semi-finals of the competition's inaugural season.
The 33-year-old has made 113 appearances across two spells at Scotstoun, as well as earning 41 caps for Scotland in his career to date.
His international honours include appearances at two Rugby World Cups, representing his country at the 2015 and 2019 tournaments in England and Japan respectively.
Reid joins the Midlands side with immediate effect, and will be available for selection for their next match.