With nearly all second round votes counted, conservative Fidesz had won 263 seats, above the 258 needed for the two-thirds majority, ousting the Socialists after eight years and securing a mandate to enact reforms and revive the economy.
"Revolution happened today in the polling booths," said Viktor Orban, the country's next prime minister.
Hungarian people today have ousted the regime of oligarchs who misused their power, and the people have established a new regime, the regime of national unity."
Fidesz was last in power between 1998 and 2002 and Mr Orban can now form the first non-coalition government with a two-thirds mandate in Hungary's 20-year post-communist history.
The newly formed far-Right Jobbik gained 47 seats, behind the ruling Socialist Party, who will have 59 deputies in the next parliament.
Fidesz, which led the governing coalition in 1998-2002, has pledged to reduce bloated national and local government payrolls, simplify the tax system, grant citizenship to ethnic Hungarians in neighboring countries and halve the number of parliamentary deputies.
Jobbik has used the economic crisis to revive traditional Hungarian scapegoating of Jewish and gipsy, or Roma, communities for joblessness and poverty.
It has close links with the Magyar Garda, or Hungarian Guard, a banned paramilitary group with insignia modelled on the Arrow Cross of Hungary's wartime Nazis.
Great news that Hungarian voters are turning away from socialist parties. Anyone who has visited the country in the last 10 years knows that it is still trying to scrape it's way to success after almost a century of chaos. The rise of Jobbik is cause for concern. The Magyar Garda (or its associates) are not people you want to be growing in power.