The Clinton couple had a 45-minute meeting with Modi, who was accompanied by External Affairs Minister Sushma Swaraj.
Both the Prime Minister and Swaraj warmly welcomed the Clintons and wished them on becoming grandparents. Swaraj warmly hugged Hillary.
Chelsea, the daughter of Bill and former Secretary of State Hillary, gave birth to daughter Charlotte last week.
Known for their love for India, Bill and Hillary were expected to discuss Indo-US engagements and the priorities of the new government in this regard.