Shrivastava had been undergoing cancer treatment at the hospital in Andheri for over 40 days.
"Mr Aadesh Shrivastava (51) expired at 12.30 am on September 5, 2015 in Kokilaben Hospital due to cancer," Dr Ram Narain of the hospital said.
Shrivastava is survived by his wife, Vijeta Pandit, a former Bollywood actress and sister of music-composer duo Jatin- Lalit, and their two sons -- Anivesh and Avitesh.
On Friday evening, Shrivastava's brother-in-law and composer Lalit Pandit had told PTI: "He has been undergoing chemotherapy but he is not responding to it. So, the doctors have stopped giving him chemotherapy. They have an alternate theory. The doctors are trying to do their best and Aadesh is fighting it bravely."
Shrivastava, who battled cancer five years ago, was diagnosed with the same disease again. He was said to be in a critical condition when he was admitted to the hospital.
"Terrible. Terrible. Terrible News. Too young to Go Aadesh Shrivastava," film director Anubhav Sinha said on Twitter. Over the course of his career, Shrivastava had composed music for over 100 Hindi films, including Chalte Chalte, Baabul, Baghban, Kabhi Khushi Kabhi Gham, Rajneeti and others.
He got his first big break with film Kanyadaan in 1993. However, the film could not be released and its songs went unnoticed.
Shrivastava delivered chart busters like Kya ada kya jalwe tere Paro, Haathon mein aa gaya jo kal, Sona sona, Shava shava, Gustakhiyaan, Gur nalon ishq mitha, Mora Piya among others.
He was a judge on the talent hunt show Sa Re Ga Ma Pa Challenge in 2005 and 2009.
Shrivastava took to direction with his short film on child prostitution, Sanaa.