It consists of Ilias Kozas (lead singer, classical and electric guitar), Dimitris Raptis (drums), Stavros Apostolidis (bouzouki, backing vocals), Giannis Bellos (bass guitar, backing vocals), Tasos Gentzis (saxophone, backing vocals) and Asterios Fragos (electric guitar, backing vocals).

[3][4] Their debut album Keep up the Rhythm, released on March 22, 2013,[5] reached triple Platinum certification[6] from Greek music industry authority IFPI.

[9] The album artwork for Koza Mostra's two studio albums, was created by Paul Hitter, who is also responsible for the majority of American punk band Gogol Bordello's artwork.

[1] On February 1, 2020 they released a single entitled "Requiem" featuring Pedro Erazo of Gogol Bordello.

[12] On September 28, 2024 the band announced on social media, that they would be doing an album preview tour in the United Kingdom, and revealing the title of their upcoming third album, Malaka.