Sushil Kumar, who was Navy Chief from 1998-2001, died at the Army Research and Referral hospital, the family said.
Kumar served with Prime Minister Atal Bihari Vajpayee from 1998 to 2001 during challenging times that included the Kargil War, hijacking of IC 814 and Operation Parakram.
Prime Minister Narendra Modi condoled the death. "Admiral Sushil Kumar will be remembered for his great service to the nation. He contributed to the strengthening of our maritime security. Anguished by his demise. May his soul rest in peace," the PMO tweeted.
He served as the 16th Chief of Naval Staff.
Former Army chief Ved Malik tweeted: "Sad to learn about passing away of my colleague during Kargil war, Admiral Sushil Kumar of Indian Navy. Always very professional and very positive. His contribution can not be forgotten. Will miss him. RIP Sushil."
An ardent admirer of PM Vajpayee, Sushil Kumar had authored a book aA Prime Minister to Remember: Memories of a Military Chief', of the huge impact that Vajpayee had on the armed forces of India.
Among the wars that he participated in were the 1965 and 1971 Indo-Pakistan wars and the Kargil war.
When he retired in 2001, he was the highest-decorated serving officer in the Indian Navy, including with the Param Vishisht Seva Medal, Uttam Yudh Seva Medal, Ati Vishisht Seva Medal and Nao Sena Medal.
( With inputs from IANS )