His death occurred on Tuesday evening in Bombay, said Deepak Namjoshi, director of the CritiCare hospital where he died, quoted by the Press Trust of India (PTI) agency.
He suffered from "multiple health problems", Namjoshi said.
In a statement, the singer-songwriter's family say they are "deeply sad" and his wife and two children wish "love and protection to his soul".
Hospitalized in Bombay for a month, "he was able to leave on Monday", according to Deepak Namjoshi.
But his health having deteriorated on Tuesday, he was again taken to hospital where "he died of OSAS (obstructive sleep apnea syndrome) shortly before midnight".
Born in West Bengal, into a family of musicians, he is credited with popularizing disco in India.
His fans danced, in the 1970s and 80s, to his hits produced for Bollywood films, such as "Chalte Chalte", "Disco Dancer" and "Sharaabi".
Always wearing chunky gold chains and sunglasses, Bappi Lahiri collaborated with Samantha Fox for the 1995 Hindi film "Rock Dancer."
He also recorded with Snoop Dogg the Punjabi title "Patiala Peg" in 2015.
The star had also lent her voice to Hindi dubbing of Hollywood film stars.
In the early 2000s, he won a lawsuit against American rapper Dr. Dre who had used the melody of one of his songs.
Indian Prime Minister Narendra Modi paid tribute to him on Twitter on Wednesday, saying his music "touched everyone, expressed many emotions wonderfully", to the point that "all generations could identify with his works".
"His vibrant nature will be missed by all. We are saddened by his passing. Condolences to his family and admirers. Om Shanti," added the Indian leader.
Bollywood star composer and singer Bappi Lahiri in April 2016 in Bombay, India STR AFP/Archives
Also on Twitter, Oscar-winning composer AR Rahman paid tribute to the "disco king of Hindi cinema".
Bappi Lahiri's voice "made millions of people dance, myself included", tweeted Bollywood star Akshay Kumar, "thank you for all the happiness you brought through your music".
© 2022 AFP