Graeme made the decision following his side's defeat by Leinster in the Pro12 play-off match .
The 35-time capped Scotland international has suffered from persistent knee problems.
"I'm sad to be leaving the Warriors but I've made the decision after receiving medical advice," said Graeme.
"My knee has been causing me problems for some time now and, after serious consideration following the play-off, I've decided it's the right time for me to stop playing professional rugby.
“I've had an amazing ten years in Glasgow and I've really enjoyed working with all the players and coaches.
"It's very exciting to see so many talented guys coming through and there is no doubt the club has a very bright future.
"Having spent my whole professional career at Glasgow, the club will always mean a lot to me."
Graeme made his international debut against Australia in 2004 and was part of Scotland's 2011 Rugby World Cup squad.
"I'm very proud and privileged to have represented my country. Ever since I can remember I always dreamed of playing for Scotland.
"There have been many amazing experiences over the years and some great memories that will stay with me for the rest of my life, such as gaining my first cap and also the series win over in Argentina.
"Whilst I am sad to have stopped playing, I am very fortunate to have had these experiences.
“I’d still like to be involved with rugby in some capacity and I will be going out to Hong Kong with London Scottish later this month to do some ambassadorial work for Scottish Rugby during the week of the first Lions game.”
Glasgow Warriors head coach, Gregor Townsend said: “Graeme has been a fantastic servant for the club and has been extremely loyal by staying here for his whole professional career.
“He is a true professional and will be missed by everyone at the club. We wish him all the best with whatever career path he chooses and he will always be welcome at Scotstoun.”