Hebbar was trained at the J. J. School of Art, Bombay. In 1949-50 he held one-man shows in London, Beron and Paris. He has exhibited in the major Indian cities and abroad including New York, Switzerland, Australia and London; participating in international exhibitions such as the Venice Biennale and the Salon De Mai, Paris. He has been honoured with several awards during the course of his long career including the Gold Medal of the Bombay Art Society in 1947, the Padma Shri in 1961, the Padma Bhushan in 1989 and was also elected Fellow of the Lalit Kala Akademi, New Delhi. His work is represented in public collections at home and abroad, including the Museum of Modern Art, Paris,. the Dresden Gallery, Germany, as well as several private collections. His works were regularly shown at the Kumar Gallery, New Delhi since 1955.