It is the final home game of the regular season at Scotstoun Stadium (kick-off 7.35pm) and Glasgow can secure a play-off place with a win against the defending champions.
30-year-old Morrison has already made 175 appearances for the Warriors since joining the club in 2003 from Glasgow Hawks and has scored 110 points.
The team will wear a special commemorative badge on their shirts for the game.
Glasgow Warriors head coach Gregor Townsend said: "This is a massive game for the club and it will also be an opportunity for the supporters to celebrate Graeme's incredible ten years here.
"He is a fantastic ambassador for the club and the standard of play he has delivered over the years is a great credit to him."
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