The band announced their split last week. They had released 15 studio albums, from 1983's Murmur to this year's Collapse Into Now.
REM's 40-track double CD compilation is called Part Lies, Part Heart, Part Truth, Part Garbage: 1982-2011 and will be released via Warner Bros on November 15.
It follows previous hits collections Eponymous, The Best of REM, REM: Singles Collected, In Time: The Best of R.E.M. 1988-2003 and And I Feel Fine... The Best of the I.R.S. Years 1982-1987
The compilation is the band's first to feature tracks from their time at IRS (1982-1987) and Warner Bros (1988-2011). It also boasts three new tracks - 'A Month of Saturdays', 'We All Go Back to Where We Belong' and 'Hallelujah' - recorded with producer Jacknife Lee.
'We All Go Back To Where We Belong' will be released to radio and made available as a download from October 18.
"Working through our music and memories from over three decades was a hell of a journey," said bassist Mike Mills.
"We realised that these songs seemed to draw a natural line under the last 31 years of our working together."
The full tracklisting of Part Lies, Part Heart, Part Truth, Part Garbage: 1982-2011 is as follows:
1. 'Gardening at Night'
2. 'Radio Free Europe'
3. 'Talk About the Passion'
4. 'Sitting Still'
5. 'So. Central Rain'
6. '(Don't Go Back to) Rockville'
7. 'Driver 8'
8. 'Life and How to Live It'
9. 'Begin the Begin'
10. 'Fall on Me'
11. 'Finest Worksong'
12. 'It's the End of the World as We Know it (and I Feel Fine)'
13. 'The One I Love'
15. 'Pop Song 89'
16. 'Get Up'
17. 'Orange Crush'
18. 'Losing My Religion'
19. 'Country Feedback'
20. 'Shiny Happy People'
1. 'The Sidewinder Sleeps Tonite'
2. 'Everybody Hurts'
3. 'Man on the Moon'
5. 'What's the Frequency, Kenneth?'
6. 'New Test Leper'
8. 'At My Most Beautiful'
9. 'The Great Beyond'
10. 'Imitation of Life'
11. 'Bad Day'
12. 'Leaving New York'
13. 'Living Well Is the Best Revenge'
14. 'Supernatural Superserious'
16. 'Oh My Heart'
18. 'A Month of Saturdays'
19. 'We All Go Back to Where We Belong'
> REM split: Five career-defining tracks - video
> REM split: Career highlights and gigs - in pictures
Watch the REM 'Nightswimming' music video below