Winger Seymour has signed for a further two years through until May 2019, while second-row Swinson has put pen-to-paper on a new three-year deal until May 2020.
Seymour and Swinson follow Stuart Hogg, Henry Pyrgos, Adam Ashe and Greg Peterson in signing new contracts with the club, while BT Sport Scottish Rugby Academy duo Lewis Wynne and Matt Smith have signed professional deals this season.
Seymour is the Guinness Pro12’s top try-scorer so far this season with eight tries, including two against defending champions Connacht and four against Leinster.
He is now a regular for Scotland with 31 caps under his belt and 14 tries, with the most recent coming against Georgia at Rugby Park in November.
Swinson, who joined the Warriors from Newcastle in 2012, has gone on to make 90 appearances and has scored 12 tries.
The 29-year-old made his debut for Scotland against South Africa in 2013 and now has 25 caps for his country.