The 27-year-old joined Glasgow from Melrose in 2011 and has scored 69 points in 22 appearances for the Warriors.
Wight said: "I've only ever wanted to stay in Glasgow and I'm very happy to have signed this new deal for next season."
He added: "There is a lot of competition for places at the club, but that is healthy as it pushes you on and makes you a better player.
"I've really enjoyed the last couple of years in Glasgow and I believe we can only get better next season."
Head coach Gregor Townsend added: "Scott is one of our most consistent performers in training and has an excellent understanding of the game.
"I'm sure he will be doing all he can to stake a claim throughout the season and seize any opportunity that comes his way."