Dutt was born on 29 July 1959 to Bollywood megastars Sunil Dutt and Nargis and was educated at The Lawrence School, Sanawar near Chandigarh. Dutt married the actress Richa Sharma in 1987. e couple have a daughter, Trishala, born in 1987, who lives in the United States with her grandparents, following a custody battle with Dutt after the death of his wife. They divorced in 2005. Dutt married Manyata (also known as Dilnawaz Sheikh) in 2008 at a private ceremony in Goa, after two years of dating. 

s a child actor, Dutt appeared in the 1972 film Reshma Aur Shera, which starred his father; he appears briefly as a qawali singer. Dutt made his Bollywood movie debut with Rocky in 1981. His mother passed away three days before the film's premiere. He went on to star in Vidhaata, the highest grossing Hindi film of 1982. In 1985 he shot for his first film in three years with Jaan ki baazi over the rest of the 1980s, Dutt appeared in successful films such as Main Awara Hoon (1983), Jeeva (1986), Mera Haque (1986), Immandaar, Inaam Dus Hazaar (1987), Jeete Hain Shaan Se (1987), Mardon Wali Baat (1988), Ilaaka (1989), Hum Bhi Insaan Hain (1989), Kanoon Apna Apna (1989), and Taaqatwar (1989).

Dutt was imprisoned for most of the next four years, while films he had worked in continued to appear from time to time. Finally released on bail in late 1997, he returned to the screen in director Ram Gopal Verma's now cult film Daud, but despite the movie taking in a phenomenal opening the film crashed and was labelled a flop by critics. He then played a supporting role in the 1998 hit Dushman.1999 was seen as Sanjay's comeback year as he started the year off by starring in the Mahesh Bhatt directed hit Kartoos along with Khoobsurat, Daag: The Fire, Haseena Maan Jayegi and, most importantly, the Award winning Vaastav: The Reality, for which he won his first Filmfare Best Actor Award. His role in 2000's Mission Kashmir won him critical acclaim and a number of awards and nominations, as did his subsequent performance in Kurukshetra. As the decade went on, he continued to play important roles in popular and critical successes such as Jodi No.1 (2001), Pitaah, Kaante (2002) and the National Award-winning blockbuster Munna Bhai M.B.B.S., which also garnered him several awards. Later successes came with Musafir (2004), Plan (2004), Parineeta (2005) and Dus. He also won critical acclaim for his perfomences in Shabd and Zinda.

The veteran actor hosted the fifth season of reality TV show, Bigg Boss on Colors.