Obama, who landed in the overcast capital at around 9:40am (0410 GMT), was accorded a red carpet welcome at the start of a visit which is seen as symbolising a new warmth in sometimes strained bilateral ties.
The two leaders are due to hold detailed talks later on Sunday on a range of issues including climate change, defence cooperation and a long-delayed civil nuclear power agreement.
Obama, who is the first US president to travel to India twice while in office, will also be the chief guest at Monday’s Republic Day parade in the capital.
The visit, which follows a summit in Washington in September, comes less than a year since the Obama administration effectively ended its blacklisting of Modi.
The Hindu nationalist had been shunned by the United States and European Union following deadly communal riots in the western state of Gujarat in 2002 while Modi was the chief minister.
In an interview ahead of his arrival, Obama hailed the “remarkable” rise of the 64-year-old Modi, the son of a tea-seller who was elected the leader last year of the world’s largest democracy.
Obama had been due to visit the Taj Mahal in the city of Agra on Tuesday, but he has scrapped that leg of his trip in order to attend the funeral of King Abdullah in Saudi Arabia.
According to protocol, the prime minister does not greet foreign leaders on their arrival, meeting them instead at a formal ceremony at the presidential palace. Modi made the decision himself to break with tradition and surprised even his own handlers, media reports said.
As Obama’s motorcade headed off for the welcome ceremony at the residence of President Pranab Mukherjee, the roads were lined with armed police and soldiers, part of a highly choreographed plan for the visit.
Up to 40,000 security personnel have been deployed for the visit and 15,000 new closed-circuit surveillance cameras have been installed in the capital, according to media reports.
The two sides have worked to reach agreements on climate change, taxation and defence cooperation in time for the visit.
The United States views India as a vast market and potential counterweight to China’s assertiveness in Asia, but frequently grows frustrated with the slow pace of economic reforms and unwillingness to side with Washington in international affairs.
India would like to see a new U.S. approach to Pakistan.
“Particularly with regards to security, and we would like a much greater understanding with the United States with regards to regional issues,” India’s Finance Minister Arun Jaitley said in Davos ahead of Obama’s visit.
Elected last May, Modi has injected a new vitality into the economy and foreign relations and, to Washington’s delight, begun pushing back against China’s growing presence in South Asia.
Annual bilateral trade of $100 billion is seen as vastly below potential and Washington wants it to grow fivefold.
The White House said Obama will depart slightly early from India to travel to Saudi Arabia following the death of King Abdullah, instead of a planned visit to the Taj Mahal.
Like Obama, Modi rose from a modest home to break into a political elite dominated by powerful families. Aides say the two men bonded in Washington in September when Obama took Modi to the memorial of Martin Luther King, whose rights struggle was inspired by India’s Mahatma Gandhi.
The “chemistry” aides describe is striking because Modi’s politics is considerably to the right of Obama’s, and because he was banned from visiting the United States for nearly a decade after deadly Hindu-Muslim riots in a state he governed.
Obama, the first sitting U.S. president to visit India twice, also enjoyed a close friendship with Modi’s predecessor Manmohan Singh, who in 2008 staked his premiership on a controversial deal that made India the sixth “legitimate” atomic power and marked a high point in Indo-U.S. relations.
The nuclear deal failed to deliver on a promise of billions of dollars of business for U.S. companies because of India’s reluctance to pass legislation shielding suppliers from liability, a deviation from international norms.
In a reminder that personal chemistry is not always enough, under Obama ties between Washington and India descended into bickering over protectionism that culminated in a fiery diplomatic spat in 2013 and the abrupt departure of the U.S. ambassador from New Delhi, who has only just been replaced. – Agencies