The pop star will be the youngest solo headliner in the festival’s history.
The group's first international album landed in July 1967, during a highly significant year for the band.
The legendary artist's new song is set for release on June 17.
The archival footage will be broadcast BBC platforms from June 25 to 27 as this year's festival was cancelled due to the pandemic.
The news comes after the band's new album, Dreamers Are Waiting, was released on June 4.
All performances will take place on the Pyramid Stage, while a maximum capacity of 49,999 people will be allowed.
Also newly-announced for the two-day event are George Ezra, DJ Honey Dijon and Róisín Murphy.
The newly-rearranged shows kick off in Glasgow on September 23, with the band also looking to reschedule further shows in Leeds and Dublin.
The duo's first official new material since 2019's acclaimed 'No Geography' will be out on Friday, April 23.
The ambitious live-streamed event on May 22 will also feature Damon Albarn, IDLES, Jorja Smith and many more.
A cryptic video was shared on the festival’s social media accounts.
The coming summer will thus be the second in a row without a Glastonbury, after the 2020 event was called off in March last year.
The archive is currently in the early stages of development, but will prospectively launch in 2021.
Michael Stipe said of R.E.M.'s performance, "we pulled ourselves back to the front of the line and proved what we’re capable of. It was a great show for us!”
The virtual festival will air on a pop-up channel from 24 to 28 June to mark what would have been Glastonbury's 50th anniversary.