Grant, a Scotland internationalist and part of last year's British & Irish Lions squad, has made 78 appearances for Glasgow since joining from Edinburgh in 2010, 58 in the RaboDirect PRO12 and 20 in the Heineken Cup.
The 28-year-old said: "I've really enjoyed my four years at the club and I'm excited about the opportunity I have at Glasgow.
"There has been so much progress, with our support getting bigger each year, our excellent facilities at Scotstoun and a really good squad."
Reid, 26, who joined Warriors from Ayr in 2011, was in the Scotland squad for the 2012 Autumn Tests and played for Scotland A in their draw with England Saxons last month.
He said: "I've really improved since turning professional and joining the club and I want to continue to learn and develop my game."
Gregor Townsend, Glasgow's head coach, said of Grant: "Ryan has worked hard over the past two seasons and has got his rewards through playing at the highest level. He delivers what we expect from our props, which is scrum dominance, strong defence, work-rate and accuracy in contact."
"His display against the Ospreys last season was one of the best individual performances of the season."
On Reid, Townsend added: "Gordon played very well for Scotland A last month and is at an age where he'll continue to develop. We will benefit from that over the next few years."