Wing Seymour, 28, has agreed a new deal until May 2019 while lock Swinson, 29, is now contracted until May 2020.
Both made their Scotland debuts in 2013 and have 56 senior international caps between them.
Fellow internationals Stuart Hogg and Henry Pyrgos have already signed new deals with Glasgow, as has former Scotland sevens player Adam Ashe.
"This is my second three-year contract with the Warriors and I've signed for that length of time because it's a great club to be at and there is a good buzz around the place," Swinson, who joined from Newcastle Falcons in 2013, told the Warriors' website.
"With other guys signing new contracts it's good to know that the guys you get on well with on and off the pitch are going to be here."
New Zealander Dave Rennie will replace Glasgow head coach Gregor Townsend in the summer, with the latter taking on the Scotland head coach job.
"It's great news that Tommy and Tim want to stay and continue their careers in Glasgow," said Townsend.
"They both work really hard to continually improve and have become important members of the squad over the last few years.
"They care a lot about the club and make big contributions both on and off the pitch."
Seymour started his professional career with Ulster, joining Glasgow in 2011. And, like Swinson, he helped Warriors win the Pro12 in 2015.
"The club has really built a big name for itself since I've been here and it's something I'm keen to remain a part of," he said.
"With the change of coaching staff next season it offers an exciting opportunity to carry on that development and really continue growing with the club.
"Dave Rennie is regarded as one of the best coaches in the world and we're all really looking forward to working with him next season."

Colin Gregg, 75, is said to have indecently assaulted four boys aged between 10 and 14 over three decades.
Leeds Crown Court heard how Mr Gregg, of Gosforth, Newcastle, who helped build the family business in the 1960s, molested boys at his home, in his car and in a swimming pool.
He denies nine counts of indecent assault.
Paul Greaney QC, prosecuting, told the court Mr Gregg concealed his true nature behind a "veneer of respectability" and despite a life of distinction was "an abuser of children."
The allegations relate to a period when Mr Gregg was a teacher and head teacher, beginning in 1963.
He has dismissed the allegations as "evil lies" motivated by money.
The jury were told of Mr Gregg's time building up the bakery chain into one of the most recognised brands on the high street and of charity work in the north-east of England.
Mr Greaney said: "On the surface Colin Gregg deserves the respect and thanks of our community.
"The prosecution case is that he was an abuser and that during two periods 20 years apart, he engaged in the sexual abuse of boys."
The trial, which is due to last two weeks, continues.
Scotland players Tommy Seymour and Tim Swinson have signed new deals to stay at Glasgow Warriors.
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The heir to the Greggs bakery business has gone on trial accused of sex offences against boys.