Prince William's wife Kate Middleton gave birth to a baby boy - the third in line to the throne - on Monday.
Extending his greetings on behalf of people of India, Mukherjee said, "The news of the safe arrival of the youngest member of the Royal family has been received with delight and happiness in India."
"On this joyous occasion, on behalf of the people and the Government of India and on my own behalf, I would like to convey my heartfelt congratulations to Their Royal Highnesses the Duke and Duchess of Cambridge.