G-Dog first signed with Glasgow in season 2003-04 and has been a regular fixture in the side's backline since moving from Glasgow Hawks.
On the first eight years of his career, Graeme said: "It seems like only yesterday that I was getting my first game for Glasgow because it's all gone very quickly.
"But I suppose that's the life of a rugby player - time flies when you're enjoying yourself.
"I believe in this team. We have a good young squad that are growing up together and I have a feeling that if the core of this squad can stay together and improve, we can do something special."
On securing Graeme's services until 2014, Sean Lineen said: "It's fantastic news. Loyalty is pretty hard to come by these days in professional rugby so it's great to have someone the quality of Graeme committing to another two years."
"I've watched him grow year on year both in stature and the way he plays the game.
"He brings a lot to the club off the field as well.
"He's a real trustworthy guy and someone that everyone else looks up to. He gives 100% on the field every time."
Graeme Alexander Morrison won his first, second, third and fifth caps for Scotland all in the same year (2004) against Australia. His first was on the 2004 summer tour when he came on as a replacement in the first Test. Earlier in the tour he had also played in the matches against Queensland Reds, New South Wales Country and New South Wales Waratahs and was heralded as the best player on the park in the Waratahs match. He scored his first international try in the historic 100-8 win over in November 2004 Japan at McDiarmid Park in Perth.
In June 2006 he made a considerable impact for Scotland A when he started at outside centre in all three matches in the Barclays Churchill Cup in Canada. Previously he was outside centre in all 10 of the under-21 internationals that Scotland played in season 2002-2003. Those honours included appearances in the IRB Under 21 World Championship in June 2003, ending with a notable 33-22 victory against England at Newbury.
A former pupil of Dollar Academy, he has studied physiology and sports science at Glasgow University. His representative rugby includes under-16 and under-18 appearances for Midland Schools and Scottish Schools and under-19 and under-21 international honours as well as Hong Kong under-16.
Graeme joined Glasgow Rugby from Glasgow Hawks in season 2003-2004 and scored a debut try in the warm-up match against Gloucester at Kingsholm. His father, Ken, played for Glasgow High School FP when the club championship was introduced to Scottish rugby in 1973, and he won a B cap against France in Bayonne in 1974 before going on to play for Hong Kong.