His original deal was due to expire next summer, but the 21-year-old has now agreed to extend his stay at the club until the summer of 2022.
The former Scotland U20 captain enjoyed a breakthrough campaign in 2018/19, scoring twice in 12 appearances in all competitions as well as earning his first professional contract.
His form across the season also saw a brace of accolades come his way; McDowall shared the March McCrea Financial Services Warrior of the Month award with fellow centre Kyle Steyn, before walking away with the Land Rover Young Player of the Season prize at the club's end-of-year Awards Dinner back in May.
A season that saw him called into a senior Scotland training squad for the first time ahead of the 2019 Guinness Six Nations also brought McDowall his first tries in a Glasgow jersey, as he crossed in a 42-10 victory away to Zebre in March, before recording his first score at Scotstoun against the Toyota Cheetahs three weeks later.
Speaking to glasgowwarriors.org, McDowall said: "I've loved my time here so far. I came through the academy here and I'm really happy to be staying.
"I just want to get as much game time as possible. There's a lot of competition for places at centre, but I just take every game as it comes.
"I'm really looking forward to being back out in front of the fans at Scotstoun. It's something I've missed over the last few months, so I'm really looking forward to hopefully playing against Ulster next month."
Glasgow Warriors Assistant Coach Jason O'Halloran, added: "Stafford had an excellent debut season as a professional last year.
"We're delighted that he is going to continue his development here at Scotstoun.
"He was quite rightly named our Young Player of the Season last year and has come into pre-season hungry and eager to learn even more.
"Stafford has a very exciting future ahead of him and it's great for the club that he is committed to Glasgow Warriors."