With nearly all second round votes counted, centre-right 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," Orban told some 4,000 cheering supporters in downtown Budapest.
"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 Orban can now form the first non-coalition government with a two-thirds mandate in Hungary's 20-year post-communist history.
The prospect of a strong government is seen by analysts as positive for the forint currency and financial markets in the short term, but Fidesz will not enjoy a long honeymoon period.
Investors will want to see clear plans on how it wants to lower taxes and also keep the budget deficit in check.
Hungary, which has a track record of deficit overshoots, stabilised its finances with painful spending cuts last year. With its public debt still at around 80% of GDP, the new government will not have much fiscal room for manoeuvre and will have to set the debt on a declining path.
"If implemented, changes like the reform of the municipal system or a profound tax and labour market reform would shift the nature of the fiscal adjustment from expenditure freezes [...] towards structural changes that would support long-term fiscal sustainability," analysts at Goldman Sachs said.
"A failure to implement the promised reforms would quickly erode the confidence in the new government and the course of the economic policy."
Government bonds and the forint have rallied in the two weeks since Fidesz secured a majority in the first round.
The central bank is seen cutting interest rates further by 25 basis points to a new all-time low of 5.25% on Monday.
The Socialists will have 59 seats in the next parliament while far-right Jobbik will have 47 seats. Green liberal LMP has won 16 seats based on preliminary results.
Its mandate would enable Fidesz to enact reforms such as streamlining local government and changing electoral law or even the constitution.
It can also make dual citizenship easier to get for millions of ethnic Hungarians in neighbouring states, which may lead to tension with Slovakia and also some other neighbours.
Fidesz has pledged to create jobs, lower taxes and cut bureaucracy to revive the economy.
It has also said it wants a new deal with international lenders - the IMF and the EU - who saved Hungary from financial collapse in October 2008.
The deal will expire by October and Fidesz will likely want to negotiate a higher budget deficit for this year, which analysts said the IMF would probably accept only if it saw a clear plan for structural reform.
Hungarians, weary of a deep recession and unemployment running at a 16-year high, will want to see an improvement in their lives quickly, and with municipal elections due in October, Fidesz will need to make some symbolic changes.
It has promised to halve the size of parliament and the number of representatives in councils and curb corruption.
"Public safety, holding corrupt leaders accountable, and most of all, jobs. That's what most Hungarians want," said Janos Fristaczki, 60, a bus driver.
Fidesz will face pressure from Jobbik to keep its promises.
"A million people expect the tax cut, a million expect that the threat of being evicted from their homes will be averted, that crime will be liquidated," Jobbik chairman Gabor Vona told supporters on Sunday.
"If the new government, breaching its election pledges, wants to water down these urgent issues, Jobbik will be ready to force its will - which in our view is the will of the whole of society - on the cabinet to be formed, using all tools in parliament and all democratic tools outside parliament."
(EurActiv with Reuters.)