Born in Moscow, USSR on December 5, 1967,[3] Kozlov studied piano at Children's Music School before switching to bass.[3] Kozlov won the Gnesin Music Academy Competition which enabled him to enter college at age 15 and study electric bass guitar.[4]
After graduation Kozlov did a mandatory two year military service where he played tuba and other brass instruments.[3] After leaving the service, Kozlov played with the Soviet state-owned "Melodia" Studio Ensemble in 1989[3][4] and in 1991 won the USSR Competition of Jazz soloists.[4] He then moved to New York City to study and perform jazz.[3]
Kozlov has played on two Grammy Award-winning albums, the first with Brian Lynch[3] and the second with Mingus Big Band (Live at Jazz Standard) in 2011.[4] Kozlov has performed as musical director of the latter band.[5]