Singh, dubbed "The Ghazal King", had been in intensive care for three weeks after undergoing surgery when he fell seriously ill with a brain haemorrhage.
Ghazals are a poetic form of singing that originated in the Middle East and spread to India from the 12th century.
They were traditionally reserved for the elite, but Singh popularised the form in the 1970s and 1980s by pioneering a modern ghazal sound and using Western instruments alongside Indian classical ones.
As well as spreading the appeal of ghazal in India, Singh sang and composed for Bollywood, the Hindi-language film industry.
Singh will be best remembered for his music in the films "Prem Geet" (Love Song) in 1981 and "Arth" (Meaning) the following year.
He last sang in the low-budget film "Khushiyaan" (Happiness), which is due in cinemas on Friday.
Jagjit Singh was born to a poor family in the north Indian state of Rajasthan on February 8, 1941.
He took to singing at an early age and like millions of other migrants, travelled to Mumbai, then known as Bombay, to make his fortune.
After initial struggles singing advertising jingles and performing at parties, he found a foothold in regional-language and Bollywood cinema, going on to form a successful duo with his wife Chitra in the 1970s and 80s.
When Singh was taken to hospital on September 23, he had been about to sing at a concert in Mumbai with Pakistani ghazal legend Ghulam Ali.
This article first appeared HERE.