The 27-year-old former Stormers and Western Province forward has agreed a one-year contract subject to a medical and will join his new club for pre-season training later this month.
Holmes, who specialises at openside but can play elsewhere along the back row, had stints in England with Northampton, Penzance and Cornish Pirates.
Holmes, whose father was born in Peebles, told his new club's official website: "I am very excited to have signed for the Warriors and I'm looking forward to the challenge.
"The Glasgow squad is young and very competitive and I want to be part of that. I can't wait to meet all the lads and start training with them.
"I've been to Glasgow before and I think it's a great city. I also have family there and I know Josh Strauss and DTH van der Merwe, so I'm sure they will help me settle in quickly.
"I like to test myself at the highest level, so I'm really looking forward to playing in the RaboDirect PRO12 and Heineken Cup next season.
"My father has always wanted me to play for Glasgow and now I have the chance to do that.
"My dream is to one day play for Scotland and if that was to ever happen my father would be the proudest man on earth, and it would be my greatest achievement."
Glasgow head coach Gregor Townsend added: "Tyrone is a low tackling and tough openside flanker, who has worked extremely hard to develop his game. He will add competition to our squad and we're looking forward to welcoming him to Glasgow."