"It is with the deepest joy that I share that Yamini and I have been blessed with a beautiful daughter. Our child was born this afternoon in New Delhi.
"My family feels truly glad and grateful for this precious gift of a girl. We have named her Anasuya," Varun said.
Varun, son of the late Sanjay Gandhi and Union Minister Maneka Gandhi, had married Yamini at the Kamkoteshwar Temple in Varanasi in March, 2011.
He is the estranged cousin of Congress Vice President Rahul Gandhi.