Greg has been capped by the USA and joined Leicester Tigers in December from Super Rugby side, NSW Waratahs. He has played three times for the Aviva Premiership side.
The Australian-born lock, who was with the Waratahs for five years after joining their Academy in 2009, has made one Super Rugby appearance.
In 2010, he made his Shute Shield debut for Manly, making his mark by winning the 2010 Shute Shield Rookie of the Year award in his first year out of school.
The towering forward, who stands at 6 foot 8 and weighs more than 19 stone, represented Australia U20s on eight occasions.
Peterson comes from a rich athletic background with his father having played American Football for Northwestern University in Chicago and his grandfather having played in one of the first ever rugby union games in the United States.
Speaking to glasgowwarriors.org, Greg said: "I worked alongside some very good second rowers at the Waratahs such as Dean Mumm and Kane Douglas, who have excelled when they've moved to the northern hemisphere.
"Gregor (Townsend) has given me the opportunity to join Glasgow and I believe I can help the team progress further.
"I've learnt a lot at Leicester Tigers about northern hemisphere rugby and I've loved my time there. I've always given one hundred percent and I'll do the same for Glasgow.
"I like the style of rugby Glasgow play and everybody works hard for each other, which is how I think the game should be played. The harder you work the more opportunities you get.
"Talking to Gregor about the values of the team and the way the team plays almost feels like a perfect fit, so when I get up there I'll grab the opportunity with both hands and show the supporters the kind of player I am."