Venkatswamy died on Monday at a private hospital in Hyderabad following prolonged illness. He was 85.
In a condolence message to his son G. Vivekanand, President Mukherjee said he was "deeply saddened" to learn about the passing away of G. Venkatswamy.
"Venkatswamy was a senior Congress leader, veteran parliamentarian, and an able administrator who served the nation in different capacities. He served with distinction as a member of the union council of ministers," the president said.
"In his death, we have lost an eminent leader who always worked for the upliftment of the underprivileged and marginalised sections of society," he added.
"Please convey my heartfelt condolences to the members of the bereaved family and Venkatswamy's countless friends and well-wishers. I pray to the Almighty to give you and your family the strength and courage to bear this irreparable loss," he said.
Known as Kaka among his supporters, Venkatswamy served as a minister in the cabinets of Indira Gandhi, Rajiv Gandhi and P.V. Narasimha Rao.
The octogenarian leader from Telangana was elected to the Lok Sabha for seven terms, the last being in 2004.