Randeep was born in the Rohtak district of Haryana. He comes from an illustrious background with his father, a surgeon, and his mother a social worker. In early childhood, he attended a boarding school in Sonepat, Haryana, and thereafter shifted to DPS RK Puram, New Delhi. Randeep then moved on to Melbourne, Australia for further studies.
He returned to India after a few years, and started working in the marketing department of an airline and but also pursued acting in theatre.
Soon after, Randeep was offered, his debut role in Mira Nair's Monsoon Wedding (2001) where he played an NRI.
However even he had a dry spell for the next 4 years after his first film. His next venture was Ram Gopal Varma's D (2005). "D" was a turning point in his career and he got acclaim for this role.
Randeep has been seen in "Karma, Confessions and Holi" (2006) produced by Drena De Niro. He played a romantic role for the first time in a movie named Ru-Ba-Ru.
He was known to be dating Sushmita Sen at one point of time.