The track - the street dancing group's debut effort - follows the release of buzz track '2 Seconds' earlier this year.
The band, comprising Chantelle, Kieran, Cassie, Pierre, Kimmy and Levon, were signed to Sony records last year and have worked with Lady GaGa's creative director and choreographer Laurienn Gibson.
Production credits on their forthcoming debut album, which is due later this year, include Wayne Wilkins (Cheryl Cole, Beyoncé), Rico Love (P Diddy, Usher) and Jim Jonsin (Eminem, Drake).
'Best Damn Night' is released on July 24. See two exclusive images of the video, which feature the group dancing around a warehouse, below: