Final unofficial election results announced by the Hungary's National Election Committee gave the opposition centre right Fidesz Hungarian Civic Party the most seats with 148 members of the 386-seat parliament.
The ruling Socialists won 134 seats, the right-wing Independent Smallholders 48, the liberal Free Democrats 24, Fidesz's centreright allies the Democratic Forum 17, and the far-right Hungarian Justice and Life Party 14 seats.
One seat went to an independent candidate, the former finance minister, Mr Mihaly Kupa.
The national turnout was 57.20 per cent, one per cent more than the first round figure of 56.25 per cent.
The result was announced with 99.89 per cent of votes counted.
It means Fidesz has 38.34 per cent of seats in parliament, the Socialists 34.72 per cent, the Smallholders 12.44 per cent, the Free Democrats 6.22 per cent, the Democratic Forum 4.4 per cent, and the Hungarian Justice and Life Party 3.62 per cent.
The 35-year-old Fidesz party leader, Mr Viktor Orban, is likely to become the country's youngest prime minister this century.
"Voters have shown that for a new century the country needs a new government," said a jubilant Mr Orban, a former student leader who looked likely to form a coalition of right-leaning parties.
The Prime Minister, Mr Gyula Horn, conceded defeat to Fidesz in a sombre news conference at Socialist party headquarters where he said: "I'd like to congratulate Fidesz for its results."
Earlier exit polls had suggested a razor-thin majority for the Socialists, successors to Hungary's former ruling communists, but their early gains were quickly swamped.