He was cheered by supporters after a victory parade from the airport.
Current PM Manmohan Singh, whose Congress party was crushed in the poll, is expected to resign later.
Mr Modi, a Hindu nationalist and chief minister of Gujarat, campaigned on promises to revive the economy.
Results show the BJP gained a majority in parliament and will be able to govern without coalition partners.
However, many Indians still have profound concerns over Mr Modi because of claims he did little to stop communal riots in Gujarat in 2002 in which at least 1,000 people died, most of them Muslims.
Mr Modi has always denied the allegations and was never charged.'India has won' Continue reading the main story Analysis Soutik Biswas India correspondent
Make no mistake, the scourge of unrelenting inflation turned the poor and the middle class against Congress: for the last three-and-a-half years India has been suffering its highest rate of inflation for 20 years, one that has also been higher than the world average.
This, many say, was the immediate trigger for people's anger and disenchantment with Congress.
Then there was what many call the party's failure to adapt to a changing India, which was moving, in the words of one commentator, from a "petitional to an aspirational culture".Read more from Soutik
After arriving in Delhi from his home state of Gujarat, Mr Modi was greeted by flag-waving supporters. He stepped out of his car, flashing a victory sign.
A brass band, drummers and bagpipers met him at the BJP headquarters, while bunting and balloons decorated the street.
Noticeably tight security is in place, the BBC's Sanjoy Majumder in Delhi reports.
Mr Modi will go to Varanasi for a ceremony by the river Ganges later on Saturday.
With votes still being counted, the BJP has won more than the 272 seats needed for a parliamentary majority.
With its allies, the party could get more than 330 seats out of 543.
"India has won, good days are about to come," Mr Modi tweeted on Friday.
He later told his cheering supporters: "In the 60-year history of Indian independence, I have never seen this in the Indian media, what you have done in our country."Narendra Modi was mobbed by protesters after he arrived in Delhi Supporters cheered as Mr Modi's car drove by on its way to the BJP Security was tight with police and special forces personnel lining Mr Modi's route
He said he would rule for all Indians.
"The real government will belong from Kashmir on top to Kanya Kumari [on India's southern tip] - that is a real government.
"The age of divisive politics has ended - from today onwards the politics of uniting people will begin."
World leaders, including US President Barack Obama and UK Prime Minister David Cameron, have congratulated Mr Modi on his victory.
India's new leader has received invitations to Washington and London. Previously, the US denied him visas and the UK cut off all ties with him following the 2002 riots.
Pakistani Prime Minister Nawaz Sharif commended the BJP's "impressive victory" in the election.