Varma (93) passed away at M S Ramaiah Memorial Hospital owing to age-related ailments, Gokula Education Foundation (Medical), founders of M S Ramaiah Educational Institutions, said in a statement.
A renowned neurosurgeon, he is survived by wife Dr Malathi Varma and sons Dr Ravi Gopal Varma and Shashi Gopal Varma.
Varma, a member of Mavelikkara royal family in Kerala, had also served as Director General of Health Services.
In recognition of his services, he was honoured with "Padmashri" in 1970.