Around 1000 tickets will be given away for the event, which is expected to be one of the highlights of the BBC Music Day event, which was held for the first time last year.
Duran Duran, Will Young, Laura Mvula and Ruby Turner are among the other acts involved in one-off concerts and shows across the UK on 3 June.
Live music will be performed on 40 iconic bridges around the UK, while bells are planned to ring out from 50 church towers simultaneously throughout towns, cities and village.
The Travis gig with the BBC SSO at the city’s most celebrated music venue will be broadcast live on Radio Scotland and the BBC iPlayer.
Travis frontman Fran Healey said: “It’s the coolest thing we’ve been asked to do, coming at a point, I feel, where we’ve hit full creative bloom as a group.
“And the fact the BBC SSO will join us on our turf at the Barrowlands - and not in their usual habitat - is something I feel the audience will love.”
Bob Shennan, director of BBC Music, said: “BBC Music Day is a unique opportunity for people to celebrate music and musical talent, whether attending one of the many events taking place or tuning in at home.”
Details of how to get tickets for the Travis gig with the BBC SSO will be announced on Radio Scotland on 9 May.