Lt Gen Jacob, who was 92, breathed his last this morning after prolonged illness, army sources said.
Born in 1923, Lt Gen Jacob is best known for his role in India's victory in the Indo-Pakistan war of 1971 and the liberation of Bangladesh.
Lt Gen Jacob, then a Major General, served as the Chief of Staff of the Indian Army's Eastern Command during the war.
Prime Minister Narendra Modi on Twitter said the country was grateful to him for his impeccable service.
Born in the Bengal Presidency under British India, Lt Gen Jacob joined the army at the age of 19 and also fought in World War II and the Indo-Pakistan War of 1965 before he retired in 1978.
RIP Lt Gen JFR Jacob. India will always remain grateful to him for his impeccable service to the nation at the most crucial moments.— Narendra Modi (@narendramodi) January 13, 2016
Post retirement, he also served as the Governor of Goa and Punjab.