The 59-times capped tight-head, enjoyed a four year spell with Glasgow from 2003 having progressed from GHA and Glasgow Hawks and the Scotland age-grade set-up.
Glasgow Warriors head coach Gregor Townsend said: "It's great to welcome Euan back to Glasgow.
"He has played at the highest level of the game over the past decade and brings with him considerable experience from his time in England and France.
"He is a proven scrummager at Test level and finished the season in great form. His tackling ability is also something that we are keen to see in a Warriors jersey.
"Euan has always been very proud of his Glasgow roots and I look forward to the contribution he can make to our pack and the positive influence he can have on some of our younger players."
Murray, who has played in both England and France since his first stint with Glasgow - moving from Northampton Saints, Newcastle Falcons, Agen and Worcester before this return - said: "I'm grateful to Glasgow for the opportunity to continue my career with a club that has always meant a lot to me.
"I am passionate about playing again for Glasgow though you only need to look at some of the talent that is at the club to understand that a lot of hard work will be necessary to take the field at Scotstoun."
Euan won his first Scotland cap against Romania in 2005 and his most recent appearance for the national team was the final match in the most recent RBS 6 Nations Championship.
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