The 28-year-old loose-head has made 58 appearances in the RaboDirect PRO12 and 20 in the Heineken Cup and his powerful displays earned him a call-up to the Scotland squad in 2012.
Grant, who made his Scotland debut in the win over Australia on the 2012 summer tour, has gone on to win 15 caps for his country and is in the Scotland squad for the RBS 6 Nations.
He was called-up to the British & Irish Lions squad for the successful series win in Australia last summer.
Ryan Grant said: "I've really enjoyed my four years at the club and I'm excited about the opportunity I have in Glasgow.
"There has been so much progress at the club recently, with our support getting bigger each year and our excellent facilities at Scotstoun, so it's a great place to be.
"We have a really good squad, which gets stronger every season and there is now so much competition for places.
"I'm really looking forward to another three years in Glasgow."
26-year-old Reid joined the club in 2011 after a number of standout performances for Ayr in the RBS Premiership and has become an integral part of the Warriors pack.
His performances earned him a call-up to the Scotland squad during the 2012 Autumn Tests and he featured for Scotland A in the draw with England Saxons last month.
He has made 44 appearances for the Scotstoun-based side.
Gordon Reid said: "I'm very happy to be staying in Glasgow for another three years.
"I've really improved since turning professional and joining the club and I want to continue to learn and develop my game.
"There is a great atmosphere around the club and we have a very strong squad, which is made up of a group of players who all work hard for each other."
Glasgow Warriors head coach Gregor Townsend said: "It's excellent news for the club that both Ryan (Grant) and Gordon (Reid) have signed up for another three years.
"Ryan has worked hard over the past two seasons and he's got his rewards through playing at the highest level.
"His display against the Ospreys last season was one of the best individual performances of the season.
"He delivers what we expect from our props, which is scrum dominance, strong defence, work-rate and accuracy in contact.
"He's also very good at staying on his feet when carrying the ball.
"Gordon (Reid) has really developed since he became a professional.
"He played very well for Scotland A against England Saxons last month and is getting closer to playing at international level.
"Gordon is a genuine, hard-working player, who takes feedback on board very well and shows a real desire to improve his game.
"He's at an age where he'll continue to develop and we'll benefit from this over the next few years.
"I'm so pleased that both players have committed their futures to Glasgow."