The song, a reworking of 'Not In Love' from the group's second album - which was released earlier this year - will be available from December 6.
The Cure frontman is known for his melodramatic and operatic style, and will bring a new dimension to the band's sound, which is typically electronic and frequently features distorted vocals.
The song will be accompanied by two other tracks from the electronic dance band which were included on the album, however they will be presented in a very different form to how they have already been, with 'Celestica' and 'Suffocation' recorded as acoustic demos.
The band - made up of duo Ethan Kath and Alice Glass - have previously told how they do not exclusively listen to dance music, and have eclectic taste while touring.
Crystal Castles are presently on tour in Europe and recently announced they will play dates in North America.