He said: "We've got a reasonably young core of players at Glasgow and it's clear to see that we have progressed, and are still progressing, as a club. The two close games against Bath and the away win over Toulouse speak volumes in terms of how far we have come. I remember playing against Toulouse in my second season with Glasgow and it's now clear to see we've come on leaps and bounds since then.
"I'm looking forward to being part of a successful Glasgow team and achieving something special with the Warriors over the coming years."
Glasgow head coach, Sean Lineen, added: "Graeme has been with us for a while now. He has matured into a good leader and wants to establish himself in the Glasgow and Scotland no.12 jerseys.
"I'm delighted he sees the progress Glasgow are making and the ambition he has to stay and win something with Glasgow."
Having originally signed for the Warriors in 2003, Morrison is one of Glasgow's longest serving players, making 106 competitive appearances and scoring 17 tries. He captained Glasgow for the first time in the recent Heineken Cup victory over Newport Gwent Dragons in the absence of Alastair Kellock who was unavailable through illness.