Clinton and his wife Hillary Clinton had a 45-minute long meeting with Modi, who was also accompanied by External Affairs Minister Sushma Swaraj.
Hillary and Swaraj warmly hugged each other.
Both the Prime Minister and Swaraj also greeted the Clintons on becoming new grandparents.
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.
The meeting comes in the backdrop of reports that Hillary may contest the US Presidential elections in 2016.
Clinton also lauded Modi for his initiative to clean Ganga river.
"Thank you 4 undertaking cleaning of Ganga. It is a sacred project and smart approach," the former American President told the Prime Minister.
