Founding members Roger Daltrey and Pete Townshend will play their double album Quadrophenia in its entirety at the SECC on June 12.
The Quadrophenia And More Tour will see the band perform all the hits from the 1973 album, as well as a selection of Who classics.
Today's announcement follows on from the band's successful North American tour, which received rave reviews from fans and critics.
Guitarist Townshend said: "I really love playing all of Quadrophenia, it's a unique piece for me.
"Roger and I now stand almost alone together, representing not only the original band, but also its Mod audience, and of course all our other early fans."
Quadrophenia peaked at No 2 in the UK album chart upon its release and is often cited as one of the greatest rock and roll albums.
A film based on the album was released in 1979 starring Sting, Ray Winstone, Trevor Laird and Leslie Ash.
Personally directed by Daltrey, the new concert version of Quadrophenia focuses on the original album and replaces the narrative used in previous stage versions.
Imagery will be projected on massive screens. These set the music in the context of the history of the band.
The Who's performance at the SECC is their only Scottish date on their 10-day tour.
Daltrey and Townshend will be joined by a host of musicians, including drummer Zak Starkey, son of Ringo Starr, and guitarist Pino Palladino, on the tour, which begins in Dublin on June 8.
Tickets, from £60, will be on sale on Friday at 9am from www.ticketSOUP.com or by calling 0844 395 4000.