Modi invited to form government
Mr Modi met with president Pranab Mukherjee after he was formally chosen by his party as the next prime minister, just days after a resounding victory in national elections.
"The president has given me a letter for swearing-in on May 26," Mr Modi said following the meeting.
Earlier, he had kissed the steps of India's parliament, where he met the newly elected politicians of his Bharatiya Janata Party (BJP). Lal Krishna Advani, the most senior party leader, nominated Mr Modi for the prime minister's post, and the politicians gave their approval.
BJP president Rajnath Singh described the occasion as historic, because an opposition party has won a majority on its own for the first time in India's 543-seat Lok Sabha - the more powerful lower house of parliament.
The BJP won 282 seats, far more than most analysts predicted, and the incumbent Congress party just 44 seats.
In his speech, Mr Modi said the people of India had placed a big responsibility on him to meet their aspirations and hope. "I am dedicating my election to the uplift of the poor, youth and women," he said.
Mr Modi fought back tears as he thanked his party colleagues and supporters for their trust.
The 63-year-old worked relentlessly to market himself as the one leader capable of waking the nation from its economic slumber, while trying to shake off allegations that he looked the other way amid communal riots in his home Gujarat state in 2002 that killed 1,000 people, most of them Muslims. Mr Modi has served as the state's top elected official since 2001.
India is in the midst of rapid socio-economic change. About 13 million young people are entering the job market each year, but not enough jobs are being created in an economy that has slowed down to below 5% in the last two years. Prices of food have spiralled , as has unemployment.
The Congress-led ruling alliance was trounced, with PM Manmohan Singh's government plagued by repeated corruption scandals while the party's 43-year-old vice president, Rahul Gandhi, failed to inspire confidence.