Partial counts showed Modi's Hindu nationalist Bharatiya Janata Party (BJP) and its allies leading in 309 seats out of 543 being contested. The ruling Congress party alliance was ahead in just 72, according to NDTV news.
Jubilant BJP supporters banged drums, lit firecrackers and waved flags outside the party's headquarters in New Delhi, as results showed Modi ahead in both the seats he was contesting, in his home state of Gujarat and the holy city of Varanasi.
Rahul Gandhi, who led the Congress campaign, was leading by a slender margin in his seat of Amethi, a family bastion that has been held in turn by his uncle, father and mother, Sonia. A loss there would spell disaster for the great grandson of India's independence leader.
With the BJP leading in 261 seats, the party was not far short of a majority on its own, confirming the findings of the most optimistic exit polls. Returns from 989 counting stations were based on partial counts, with no results yet declared.
"This is undoubtedly going to be a BJP government," said Prannoy Roy, head of NDTV news and a political analyst.
Such an outcome would open the way for Modi, 63, to become prime minister and act quickly to form the core of a new government by naming loyalists to the prized cabinet posts of finance, home, defence and external affairs.
"We didn't go by the exit polls. We went by the sense on the ground," said Piyush Goyal, BJP treasurer.
"It looks pretty bleak at the moment," said Abhishek Manu Singhvi, a Congress leader, adding he would wait for final results.
Betting on a Modi win, foreign investors have poured more than $16 billion into Indian stocks and bonds in the past six months and now hold over 22 percent of Mumbai-listed equities - a stake estimated by Morgan Stanley at almost $280 billion.
Indian markets got off to a roaring start, with the rupee breaking below 59 to the U.S. dollar, a near 10-month high, and benchmark stock indexes up 6 percent.
Since being named as his party's candidate last September, Modi has flown 300,000 km and addressed 457 rallies in a slick, presidential-style campaign that has broken the mould of Indian politics.
In so doing, Modi has outclassed Rahul Gandhi, 43, while burnishing his pro-business record as chief minister of the western state of Gujarat.
Prime Minister Manmohan Singh, who as finance minister launched reforms in 1991 that brought an end to decades of economic isolation, has already bid farewell to his staff after a decade in office marked by mounting policy paralysis.
Modi's mantra of development has won over many voters sceptical about his Hindu-centric ideology and role in sectarian riots in his home state in 2002 in which more than 1,000 people, mainly Muslims, died. He has denied any wrongdoing and a probe ordered by the Supreme Court has found he had no case to answer.
The official count showed the BJP winning 37 percent of the popular vote, double its 2009 share. Under India's first-past-the-post system, that may be enough for the BJP to sweep battleground states like Uttar Pradesh, where it led in 57 of 80 seats.
Modi has promised that, if elected, he would take decisive action to unblock stalled investments in power, road and rail projects to revive economic growth that has fallen to a decade low of below 5 percent.
Tax and labour market reforms, backed by a gradual opening up to foreign investment, would seek to create the 10 million jobs that Asia's third-largest economy must create every year to employ young people entering the workforce.
Modi watched the results on TV at his home in Gujarat, and was due to meet his mother, 95-year-old Hiraben, soon after results become clear.
"My blessings are there. The country will develop. My blessings are there," she said.
He was later expected to embark on a victory tour to his local constituency of Vadodara, while party workers in New Delhi hoped he would later fly to New Delhi for what could be a hero's welcome.
Rounding off his journey to power, Modi may at the weekend visit Varanasi, the 3,000-year-old city that is one of Hinduism's most venerated cities, to bathe in the river Ganges in an act of ritual purification.