The opposition Hindu nationalist BJP party has promised "good times ahead" as early results suggest it is on course for a landslide victory
Although final results are not expected until later, the scale of the predicted victory is such that the ruling Congress party has admitted defeat.
BJP leader Narendra Modi tweeted: "India has won. Good times ahead."
This is the most resounding victory for a political party in 30 years, say correspondents.
Mr Modi, formerly chief minister of the western state of Gujarat, is seen as a no-nonsense, can-do leader who stands for development and muscular nationalism, the BBC reported.
He campaigned on promises of a revival in economic growth.
But many Indians still have profound concerns over Mr Modi because of claims he did little to stop the 2002 communal riots in Gujarat, in which at least 1,000 people died, most of them Muslims - allegations he has always denied and over which he was never charged.
The election result will be a crushing blow to the Congress party, which is led by the Nehru-Gandhi family and has dominated Indian politics since independence.
It reflects voter anger with Congress, which has been mired in serious corruption scandals and whose leadership has been considered ineffective in recent years, analysts say.
India's Prime Minister Manmohan Singh rang Mr Modi to congratulate him on his victory.
The 63-year-old Mr Modi celebrated with a visit to his elderly mother in Gandhinagar, the state capital of Gujarat.
Latest election results showed that the BJP is on course to win 277 seats, surpassing the 272 seats needed to secure a majority in the lower house of parliament.
With their allies, the party could achieve more than 300 seats.
Meanwhile, the Congress party - which has been in power for the past decade - is leading in fewer than 50 seats.
Accepting defeat, the Congress Party spokesman, Shakil Ahmed, said: "We are accepting the people's verdict in all humility.
"Trends of the counting are certainly not in our favour. The trends point out that the country has decided to vote against us," he was quoted by news agency AP as saying.
Even before the Congress party's announcement, there were scenes of jubilation outside the BJP's headquarters. Firecrackers exploded and people handed out sweets.
"It's a turning point for India," BJP leader Siddhartha Nath Singh told the BBC.
More than 500 million people voted in what is the world's biggest exercise in democracy.
Voter turnout in the mammoth nine-phase general election was a record 66.38%, beating the previous 1984 poll record.