Due to an official soundtrack not yet existing, I have compiled a list of the songs that were used in BattleBlock Theater. I have tried to link to these songs "as close to the source" as possible. Some of the songs are also slightly different versions to those used in the game, so once the soundtrack is released I do advise you to buy it.

I have tried to make as complete a list as I can, but as these were made by various artists it's not a straightforward process. Any additional information to make this list more complete or accurate is appreciated.

Thanks to Lindsay @ The Behemoth for giving me the list of artists.

This list is grouped by artist.

Menu Theme
https://www.youtube.com/watch?v=Y0u9Hs5fgzE

Wicked Mummy
Panic Version
Laidback Thrills
Tenorius
Dream of Freedom
https://patric-catani.bandcamp.com/album/video-game-music

Watermelon
http://www.cdbaby.com/cd/danpaladin

(Download links in the descriptions)
Mr. Finale
https://www.youtube.com/watch?v=GUW6SuHPYwo
Secret Stage
https://www.youtube.com/watch?v=T37eZ55Hcmc
Buckle Your Pants
https://www.youtube.com/watch?v=wuIbdMZ_tfY

Sally Port
Lance El Disco
Relationship Song
https://leeladouceur.bandcamp.com/music

Ant Farm
http://kidkoala.com/category/free-radio-music-library/music-library/

Other artists were Ian Moreno, Georgy Zheryakov and Matthew Harwood, but I have been unable to find any of their music that was used in BattleBlock Theater.