Jacob, who was also Governor of Punjab and Goa, breathed his last at the Army Hospital here at around 8 am.
He was admitted to the Army's Research and Referral Hospital since January 1 after suffering from pneumonia.
Prime Minister Narendra Modi condoled his demise and said India will always remain grateful to Jacob for his impeccable service to the nation. He also recalled his association with him.
"Lt Gen JFR Jacob and I interacted often. Had a memorable interaction when he presented his autobiography to me," he tweeted.
Defence Minister Manohar Parrikar and BJP chief Amit Shah have also condoled his demise.
Army chief Gen Dalbir Singh Suhag expressed his deepest condolences towards this great loss, a statement by the Army said.
He said that Jacob was a pillar of military leadership and personified the best qualities of a soldier and a statesman who will always be remembered as one of the most prominent Leaders in the annals of Indian military history.
Born in 1923 in Bengal Presidency under British India, Jacob joined the army at the age of 19 in 1942 and also fought in World War II and the Indo-Pakistan War of 1965 before he retired in 1978.
Post retirement, he joined BJP and headed its ex-servicemen wing. He was appointed Governor of Goa during Vajpayee government and then Governor of Punjab. He was also the Administrator of Union Territory of Chandigarh.
He authored two books - 'Surrender at Dacca: Birth of a Nation' and 'An Odyssey in War and Peace: An Autobiography Lt Gen J F R Jacob'.
