The 22-year-old second-row spent a month on loan with the Warriors earlier this season and impressed the coaching staff with his performances in the victories over Dragons and Zebre.
A product of the Fosroc Scottish Rugby Academy, Davidson signed for Falcons in 2016 and has made 14 appearances during his time in England.
Standing at two metres tall and weighing 115kgs, the dynamic lock has represented Scotland at U16, U18 and U20 age-grade levels.
Before moving south, he attended Kelvinside Academy in Glasgow and played club rugby for Glasgow Hawks in the Tennent’s Premiership.
The two-year deal will see Davidson playing his rugby at Scotstoun until at least 2022.
Speaking to glasgowwarriors.org, Andrew Davidson said: “I’m delighted to be returning to Scotland and to Glasgow Warriors. I thoroughly enjoyed my month up there earlier this season, so when I knew they were interested in signing me permanently it was an easy decision to make.
“Glasgow have shown this season that they’re one of the top sides in Europe and I’m excited to challenge myself at the highest level. As a Glasgow boy it feels like I’m coming home and I can’t wait to represent my city again playing for the Warriors.”
Glasgow Warriors Assistant Coach Jonathan Humphreys said: “We were really impressed with Andrew during the month he spent here. He’s physical in both attack and defence and has a strong set-piece game too.
“Having lost Greg Peterson to Bordeaux earlier this season he’ll add to our strength in depth at lock and he’ll learn a lot competing alongside the likes of Scott Cummings, Jonny Gray, Rob Harley and Tim Swinson.”