Davidson, 23, made his Glasgow Warriors debut off the bench against the Dragons in September 2018, while on loan from Newcastle Falcons. He joined Glasgow Warriors on a full-time contract ahead of the 2019/20 season and made eight appearances in total for the club.
Glasgow Warriors Managing Director Nathan Bombrys said: "We thank Andrew for his contributions over the past couple of seasons since returning to Glasgow. We wish him all the best on the next step of his career."
Marshall Sykes has signed a pro deal for Edinburgh having been aligned to Glasgow Warriors as a Stage 3 FOSROC Scottish Rugby Academy player and FOSROC Super6 Club, Ayrshire Bulls.