Kapoor, who acted in huge hits like Deewar and Kabhie Kabhie, had been ill for some time and was in hospital, reports BBC online.
He was a member of the Kapoor dynasty, which has dominated the Hindi film industry for decades.
He won several national film awards and was awarded the Padma Bhushan civilian honour by the Indian government in 2011. He also acted in a number of British and American films.
The actor was married to late English actress Jennifer Kendal, with whom he set up Mumbai's iconic Prithvi Theatre in 1978. Kapoor began his career as a child actor and appeared in more than 150 films, including a dozen in English.
He became known internationally for his roles in productions like "Shakespeare-wallah" and "Heat and Dust".
In 2015, he was given the prestigious Dada Saheb Phalke Award, the highest honour in Indian cinema. Kapoor was known for his charming smile and was often described by his fans as the "handsomest star ever".
He was cast alongside superstar Amitabh Bachchan in some of the biggest Bollywood blockbusters of the 1970s and 1980s, and the two actors played brothers, best friends or rivals.
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