He is survived by his sons Karan and Kunal and daughter Sanjana.
In a career spanning over four decades, the actor appeared in more than 150 films, including a dozen in English.
In 2015, he became the third in his family to be honoured with the Dadasaheb Phalke Award, the highest honour in Indian cinema.
Kapoor, who had a huge fan following among women, was known for his charming smile and was often described by his fans as the 'handsomest star ever'.
The legendary actor was married to late English actress Jennifer Kendal, with whom he established Prithvi Theatre in 1978.
Kapoor started his career as a child actor in the late 1940s appearing in commercial films including 'Sangram' (1950) and 'Dana Paani' (1953). He worked in four Hindi films as a child artiste from 1948 to 1954.
His first leading role was in the award-winning 1961 'Dharmputra', directed by Yash Chopra, which was one of the first Indian features to deal with partition.