The Hindu nationalist Bharatiya Janata Party captured a commanding lead for at least 272 seats in the lower house of Parliament, the majority needed to create a government without forming a coalition with smaller parties. The Congress party trailed well behind with leads in only 42 seats, its worst showing ever.
Full results are expected later in the day but it's unlikely that Modi's party would see a significant reversal, putting him on track to be the next prime minister.
With a note of triumph, Modi tweeted: "India has won!" as the results came out.
Television channels showed an emotional Modi meeting his mother and touching her feet, a traditional gesture when Hindus seek the blessings of an older relative.
His mother then marked his forehead with vermilion and fed him sweets.
The BJP's slick and well-financed campaign promised a revival of economic growth, and took advantage of widespread dissatisfaction with the Congress party, plagued by scandals and led by a young scion of India's Nehru-Gandhi family who was seen as privileged and out of touch with the people.
The Congress party, which has been at the center of Indian politics for most of the country's history since independence from Britain, conceded defeat.
"I admit that in 2014 the result is worse than our worse-case scenario. The result is a shock. But the Congress party has a deep reservoir of strength," party leader Jairam Ramesh said.
Outgoing Prime Minister Manmohan Singh called Modi to congratulate him, his office said, adding that Singh would send his resignation to President Pranab Mukerjee on Saturday.
At BJP headquarters in New Delhi, workers handed out sweets, set off firecrackers and danced outside in the streets. BJP President Rajnath Singh congratulated party workers for what he described as a "historic victory."
"In the history of independent India, no political party has defeated the Congress party with such a wide margin," Singh told a news conference that opened with the blowing of a conch shell, a traditional start for most Hindu rituals.
There was a record turnout in the election, with 66.38 percent of India's 814 million eligible voters casting ballots during the six-week contest, which began April 7 and was held in stages across the country. Turnout in the 2009 general election was 58.13 percent.
Final results were to be announced later Friday. If the BJP stays ahead of the 272-mark it would be the first time a single party has won a majority since the 1984 national election.
Exit polls by at least six major Indian TV stations had predicted a BJP-led coalition would win between 249 and 289 seats in the 543-seat Lok Sabha, or lower house of Parliament.
The Nehru-Gandhi family, which has ruled India for all but 10 years since the country won independence from British rule in 1947, was suffering its worst-ever political drubbing.
The Congress party attempted to position its 43-year-old leader, Rahul Gandhi, as youthful and capable of boosting the country's struggling economy. But many Indians see him as being out of touch with reality. His privileged background has made him appear aloof and removed from the concerns of most people.
In comparison, Modi's campaign was seen by many as a media and marketing coup for a man whose background ties him to bloodshed in his home state of Gujarat, where communal rioting in 2002 left more than 1,000 people dead, most of them Muslims. Modi is accused of doing little to stop the rampage, though he denies any wrongdoing and has never been charged with a crime.
He managed to hammer away at Gandhi — specifically the perception that he is nothing more than a feudal prince from a family that views ruling the country as its birthright.
In sharp contrast to the street parties outside the BJP office, a sober scene played out in front of Congress headquarters, where few showed up despite barricades erected to protect supporters from passing road traffic.
One small group of women sat on the sidewalk, lighting a ritual prayer fire to invoke divine help for the party while a handwritten sign standing by read, "May Rahul Gandhi be the next prime minister."
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