Sudarshan, 81, is survived by a brother and sister.
The ex-RSS chief, who had arrived in the city two days back, died at the RSS office here at 6:50 am. He was in the city for a book launch function.
Sudarshan had gone for an early morning walk and suffered a heart attack while doing Pranayam in his chamber in the RSS office, doctors said.
His body is being taken to the RSS headquarters in Nagpur and will be kept there for the people to pay their last respects, RSS members said. His last rites will be performed on Sunday at 3 pm in Nagpur.
Born on 18 June, 1931 in Raipur, he did his Bachelor of Engineering in Telecommunications.
A known votary of swadeshi, he served as Pracharak of Rashtriya Swayamsevak Sangh (RSS) for six decades and became its Sarasanghachalak in 2000 succeeding Rajju Bhaiya. He stepped down from the post due to poor health.
A native of Kuppalli village in Mandya District of Karnataka, Sudarshan was known among the Sangh workers for his physical training.
He was known for making polemical statements against BJP leaders. After the 2004 defeat of the party in the Lok Sabha elections, Sudarshan had suggested in an interview that old guards like Atal Bihari Vajpayee and LK Advani should give way to younger leadership.
During his tenure, Sudharshan, who was the first RSS chief from the south, stressed on economic sovereignty and construction of the Ram Temple in Ayodhya.
In August, he had briefly gone missing during his morning walk in Mysore.