The 22-year-old joined Warriors in 2010 and has become an increasingly key member of Sean Lineen's squad.
He claimed the RaboDirect Man-of-the-Match award for an outstanding contribution in the 31-3 win over Cardiff Blues at Firhill last Friday.
Dunbar's new two-year extension with Glasgow commits him to Warriors until at least the end of May 2014. And the player said: "I'm delighted to have signed a new contract.
"We're in a good place at the moment, and the team and club as a whole are in a strong position to make further progress in the next couple of years.
"I've really enjoyed working with and learning from the players and coaches at the club – the performances we've put in this season show just how good an environment has been created. There's a great buzz around the whole club about the opportunity we have to finish strongly in the RaboDirect Pro12, and everyone is determined to keep winning for ourselves and the supporters."
Dunbar's outstanding form at centre put Cardiff's British Lions star Jamie Roberts firmly in the shade last time out as he set up the third and fourth tries in the bonus-point defeat of the Blues.
Warriors head coach Sean Lineen said: "I'm really happy that Alex has decided his future is with the Warriors.
"His ability has always been clear, and he's now benefiting from getting a run in the side to prove to that he can more than hold his own at this level.
"There's plenty more to come from Alex if he keeps working hard at his game, and I'm delighted the Warriors are going to feel the benefit of that."
lFormer Scotland coach Sir Ian McGeechan is to leave his post as director of rugby at Bath at the end of the season.