Founding members Roger Daltrey and Pete Townshend will play the album, which became the soundtrack to the movie of the same name, in its entirety at the SECC.
The move comes two years after lead singer Roger Daltrey brought The Who's 1969 rock opera Tommy to Glasgow.
It is a far cry from the band's first ever Scottish gig at a working men's club in Greenock in the early 60s. Daltrey once said of the venue: "It was rough there".
While the iconic movie starred Sting, Phil Daniels and Ray Winstone, the new concert version focuses on the original album and replaces the narrative used in previous stage versions with powerful imagery which will be displayed on a collection of massive screens.
The Quadrophenia And More Tour will also see the band play a selection from their extensive back catalogue, ranging from My Generation and Substitute to Squeeze Box and You Better You Bet. Tickets are priced from £60.
It 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.
"We plan to close the show with a few of the really well-known anthems, and maybe some last-minute surprises. These will be as much a surprise to me as to our audience because this is an area I tend to leave to Roger; he's very good at it."
Quadrophenia peaked at No 2 in the UK album chart on its release and is often cited in lists charting the greatest ever rock 'n' roll albums.
The gig will feature some powerful images shown on huge screens all over the SECC, aiming to replace the narrative used in previous stage versions of the 1973 album.
The two original members of the band will be joined on stage by Ringo Starr's son Zak Starkey on drums and Townshend's younger brother Simon Townshend on guitar and backing vocals.
The Who's performance at the SECC on June 12 is their only Scottish date on their 10-date tour, which starts in Dublin on June 8.