The 22-year-old has represented Scotland at under-17, 18 and 20 level and made his debut for Edinburgh against Munster in the European Cup last season.
Allan has made just three substitute appearances in the RaboDirect PRO12 and is raring to get going at Scotstoun.
"This is a great move for me. I've learnt a lot over the last couple of years in Edinburgh and I'd like to thank them for everything they've done," he told the Warriors website.
"I'm ready to make the step up and I'm delighted to have signed a professional contract with the Warriors.
"I really enjoyed working with Shade (Munro) and Kenny (Murray) when I was part of the Scotland A squad earlier this year and I'm looking forward to working with them again, along with the other coaches at Scotstoun.
"This is a great opportunity for me to continue my development and I'm ready to work hard and make the most of it."
Warriors coach Gregor Townsend is excited at the prospect of having Allan on board and believes the youngster can make a push for the first team next season.
"In signing Alex, I believe we've secured a player with real quality, who is young and hungry to learn," he said.
"Alex was a stand-out performer at age-group level and has developed over the last couple of years.
"I've been impressed with his performances this season and how well he has developed as a scrummager.
"He was rewarded with a Scotland A cap in January and made a big impact when he came off the bench in that match.
"Alex is exactly the type of player we want to bring to the club and will add competition to our front row next season."
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