The former bureaucrat was not keeping well for some time. He passed away early morning on Monday, a senior Indian Administrative Service officer said.
Subramanian, a 1961-batch IAS officer of the Uttar Pradesh cadre, was a prominent face on television debates. He spoke vociferously on matters related to the bureaucracy.
He served in various posts in the UP cadre and at the Centre.
As cabinet secretary, Subramanian worked with three prime ministers -- Atal Bihari Vajpayee, Inder Kumar Gujral and H D Deve Gowda.
He was cabinet secretary from August 1, 1996 to March 31, 1998.
Subramanian was part of a group of former bureaucrats that filed a Public Interest Litigation (PIL) in the Supreme Court seeking a mechanism to insulate the bureaucracy from political interference.
On his public interest litigation, the top court had in 2013 directed the Centre and the states to set up a Civil Services Board to decide on transfers of officers of all India services -- Indian Administrative Service (IAS), Indian Police Service (IPS) and Indian Forest Service (IFoS).
The apex court had also asked the Centre to put in place a fixed-tenure policy to insulate bureaucrats from frequent transfers mainly through political interference.
Even after he retired as Cabinet Secretary in 1998, Subramanian remained active for bureaucrats' cause.
He was part of central government committees on various matters, including the one on the new education policy.
He led a task force set up by Prime Minister Narendra Modi to leverage the post office network in the country to enhance the role of India Posts in the financial inclusion.
Subramanian penned three books on Indian polity and administration.
'Extremely shocked to hear the sad news of the demise of T S R Subramanian. He was the tallest amongst all and is a big loss for the IAS fraternity and the nation. Deepest condolences to all family members. We hope and pray that your ideas and thoughts will continue to guide us,' the IAS Association tweeted.
Prime Minister Narendra Modi, former President Pranab Mukherjee, several Union ministers including Nirmala Sitharaman and Jitendra Singh, and a number of bureaucrats took to Twitter to condole Subramanian's demise.
'Shri TSR Subramanian distinguished himself as an outstanding civil servant. He also left a mark with his prolific writings and interventions on important public causes. Saddened by his demise. My thoughts and prayers are with his family and friends,' the PM tweeted.
Mukherjee also conveyed his deepest condolences to Subramanian's family and friends.
'Saddened at the passing away of Shri TSR Subramanian, Former Cabinet Secretary. My deepest condolences to his family and friends,' the former president said.
'Former Cabinet secretary T S R Subramanian is no more. Saddened by the news. He was affable, full of ideas and energetic. In many a debate on TV channels, shared thoughts with him. Condolences to his family and his fraternity,' Sitharaman said.
Minister of State for Personnel Jitendra Singh said he was saddened by news of the demise and sent his condolences to the entire IAS fraternity and the family.
Secretary, Department of School Education and Literacy, Anil Swarup, said: 'Bichde sab bari bari (all left one by one).'
"One of the most outstanding officer T S R Subramanian is no more. Rest in Peace. RIP," he said on Twitter.
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