Sehgal had been unwell for several days and died from a cardiac arrest at a hospital in the Indian capital New Delhi, according to her daughter Kiran.
The actress was dubbed The Grand Old Lady of Bollywood during her career that spanned seven decades. She is most famous in her native country for films including Cheeni Kum, Dil Se (From the Heart) and Hum Dil De Chuke Sanam (I Have Given My Heart, Darling).
She also starred in British sci-fi series Doctor Who in the 1960s and Keira Knightley's 2002 soccer drama Bend It Like Beckham.
Chopra paid tribute to the actress on Twitter.com, writing, "102 n (and) a legacy that will always be a part of Indian cinema. It was an honour to know #ZohraSehgal and to be a part of films while she was. Rip (rest in peace)."
Veteran actor Bachchan added about his Cheeni Kum co-star, "What a journey and what an immensely loveable co-star! Prayers for her blessed soul!!"
India's Prime Minister Narendra Modi also wrote on the site, "Zohra Sehgal made a mark through her acting, which is admired across generations. Saddened on (sic) her demise."