"We saw a revolution in the polling stations," he said.
"Fidesz Hungarian Civic Alliance and the Christian Democrat Party have gained 68 per cent of mandates in parliament."
He said his party will now work to rebuild the recession-hit country and make it strong again.
The Fidesz party, last in power between 1998 and 2002, had won 52.7 per cent of the votes and 206 parliamentary seats in the first round of voting on April 11, giving it the right to form the new government.
But in Hungary's complex electoral system, some 2.5 million voters went to the polls again, in 57 constituencies where no clear winner emerged two weeks ago.
Turnout on Sunday was much lower than in the previous round, reaching 44.17 per cent compared to the previous 64.29 per cent.
Fidesz, running on a joint ticket with the small Christian Democrats, can now form the country's first non-coalition government with a two-thirds mandate in Hungary's 20-year post-communist history.
"We now have the opportunity to create an unparalleled unity and, with it, initiate changes unprecedented in both their scale and swiftness," Orban had told Hungary's Magyar Nemzet newspaper on Friday.
"The entire country feels that it can now make history and this sentiment is a tremendous driving force."
The last time any government secured a two-thirds mandate was in 1994 when the Socialists teamed up with the liberal Free Democrats.
Tax cuts pledged
Fidesz has pledged more jobs, less bureaucracy and lower taxes to revive the economy. But with a history of high deficits and the budget under the microscope of international lenders, the room for fiscal stimulus will be limited.
At a news conference after the first round of voting, Orban promised to "put Hungary on the path of economic growth", pledging "substantial tax cuts already by this year".
Hungary was one of the countries hardest hit by the global recession and had to be bailed out to the tune of 20bn euros by the International Monetary Fund, the World Bank and the European Union. That rescue package came with stringent conditions attached.
Even Laszlo Kover, Orban's closest collaborator, said "it is clear that taxes won't be cut this year, but towards the end of our four-year term".