Minutes after he was sworn in a new website of the Prime Minister's Office was launched with a short first message from Mr Modi. "On 16th May 2014 the people of India gave their verdict. They delivered a mandate for development, good governance and stability. As we devote ourselves to take India's development journey to newer heights, we seek your support, blessings and active participation." (Prime Minister Narendra Modi's Message to India)
The new PM also said, "Together we will script a glorious future for India. Let us together dream of a strong, developed and inclusive India that actively engages with the global community to strengthen the cause of world peace and development." He promised in his signed message to use the "website as a very important medium of direct communication between us."
Mr Modi invited leaders from eight South Asian neighbours to his swearing-in ceremony, including Pakistan Prime Minister Nawaz Sharif, an unprecedented gesture that was as much a show of his determination to be a key player on the global stage as a celebration of his stunning election victory 10 days ago.
At Rashtrapati Bhavan, Mr Sharif sat next to Mr Modi's predecessor, Manmohan Singh. On Dr Singh's other side was Hamid Karzai, President of Afghanistan. Sri Lankan President Mahinda Rajapaksa, Mauritian Prime Minister Navinchandra Ramgoolam, Nepal's Prime Minister Sushil Koirala, Prime Minister Tshering Tobgay of Bhutan and Bangladesh parliament Speaker Shirin Sharmin also attended. (At President's Dinner for SAARC Leaders, a Pan-Indian Menu)
After the ceremony, Mr Sharif was the first to shake hands with the new Prime Minister.
In the audience were two former presidents, Sonia and Rahul Gandhi of the defeated Congress, top industrialists, Bollywood actors and saints and seers in saffron robes.
Ms Swaraj will be Minister for External Affairs.
On Sunday, Mr Modi promised that he would head a lean Cabinet with a focus on "minimum government and maximum governance". On Monday evening, after he had seen off visiting dignitaries and the crowds began to melt, the PM posed for a group photo with his team - at 45 ministers the leanest council of ministers yet. (What No One Told You Yet About Modi's New Cabinet)
There are 23 ministers of Cabinet rank, 10 Ministers of State with Independent charge and 12 Ministers of State in the new union council of ministers. The oldest is Najma Heptulla, 74, the youngest Smriti Irani, 38.
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