He is the son of Yash Chopra (legendary director and producer) and brother of Aditya Chopra (director of Dilwale Dulhania Le Jayenge and Mohabbatein). He is associate director when it comes to his father's and brother's movies.
He made his debut under his brother's direction in Mohabbatein. He starred with Amitabh Bachchan, Shah Rukh Khan, Aishwarya Rai, and five other debutantes (Shamita Shetty, Jugal Hansraj, Jimmy Shergill, Preeti Jhangiani and Kim Sharma). The film was a hit but the audiences noticed Bachchan, Khan, and Rai rather than Uday and the other five stars. However the film established him in the industry.
He has mostly done films under his father's production house. He had his first hit in 2004 with the action thriller Dhoom. His playful performance was appreciated and it enhanced him in the industry. His friend is actor Hrithik Roshan.
He dated actress Tanisha Mukherjee, his co star in Neel and Niki but unfortunately they broke up in 2007. There were many rumours about there marriage but nothing materialized.
He has worked as an assistant director in the past under the Yash Raj Film banner. His debut was the Yash Raj Film Mohabbatein starring Amitabh Bachchan, Shahrukh Khan, Aishwarya Rai and four other debutantes. The film did well at the box office and was a hit.
The movies which he has done are mostly with his father?s production house. After Mohabbatein he appeared in many more movies like Mujhse Dosti Karoge (2002), Mere Yaar Ki Shaadi Hain (2002), Supari and Charas. His first hit was Dhoom (2004) which was an action thriller and then he starred in it?s sequel Dhoom2 released in 2006. He has also worked as an executive producer for movies like Hum Tum and Dilwale Dulhaniya Le Jayenge and as a producer for Yeh Dillagi.
He is currently playing a major role in the Information Technology and digital rights management of the Yash Raj Productions and helping his brother Aditya to run the company.