President Mikheil Saakashvili has admitted his party has lost Georgia's parliamentary election, in a live TV announcement.
He said the Georgian Dream bloc of his main rival, billionaire tycoon Bidzina Ivanishvili, had won Monday's election.
Victory for Mr Ivanishvili means the first democratic transfer of power in Georgia's post-Soviet history.
Mr Ivanishvili said the "only right decision" would now be for Mr Saakashvili to resign.
While Mr Ivanishvili, 56, is set to become prime minister, his rival, who has led the country since 2003, is due to remain in power until presidential elections next year.
Under agreed reforms, the parliament and prime minister will acquire greater powers than the president after that election.
With results in from 72% of polling stations, Georgian Dream led the party list vote, which accounts for 77 of the 150 seats, with 54% of the vote. The president's United National Movement was on 41%.
The rest of the seats are made up of 73 constituencies elected by a first-past-the-post vote.
President Saakashvili said it was clear that Georgian Dream had won a majority.
Earlier Mr Ivanishvili, Georgia's richest man, had already declared victory.
In his TV address, Mr Saakashvili said he would respect the Georgian people's decision, and his party would become "an opposition force".
"It's clear from the preliminary results that the opposition has the lead and it should form the government - and I as president should help them with this."
The US congratulated Georgians on the "historic milestone" of their parliamentary election and praised the president's response to the result.
In a later news briefing, Mr Ivanishvili called on Mr Saakashvili to admit he would not be able to retain power, to resign and call a snap presidential election.
Mr Saakashvili, a pro-Western leader who champions the free market, has warned that the Georgian Dream bloc will move Georgia away from the West and back into Moscow's sphere of influence. Russia defeated Georgian forces in a brief war in 2008.
But in his briefing Mr Ivanishvili said both normalisation of relations with Russia and membership of Nato would be pursued.
"If you ask me 'America or Russia?', I say we need to have good relations with everybody," Mr Ivanishvili said according to AFP news agency.
Mr Ivanishvili made his fortune in Russia in the early 1990s, with stakes in the metals industry, banking and later property, including hotels. Forbes business website estimates his wealth at $6.4bn (£4bn).
His success was welcomed in Moscow where Prime Minister Dmitry Medvedev said it would mean more "constructive forces" entering parliament.
Vyacheslav Nikonov, deputy head of the parliament's international affairs committee in Moscow, said that in the eyes of both Mr Medvedev and President Vladimir Putin the Georgian president was a war criminal.
"Anything that would keep Saakashvili further away from the instruments of power is a plus for Russian-Georgian relations."
Landmark for Georgia
The BBC's Damien McGuinness in Tbilisi says it is a momentous day for Georgia - a day which strengthens the country's democratic credentials. Georgia has experienced much political turmoil since the collapse of the Soviet Union in 1991.
The ugly election campaign had polarised the country and there were fears that the results would be disputed, our correspondent says.
Observers from the European security organisation OSCE said that "despite a very polarising campaign the Georgian people have freely expressed their will".
Georgia's Central Electoral Commission (CEC) said there had been no grave violations during the voting.
More than half of the country's population has no proper job. Older and poorer Georgians, in particular, are struggling and some feel nostalgic about the Soviet Union.
The OSCE said the election process had "shown a healthy respect for fundamental freedoms... and we expect the final count will reflect the choice of the voters".
However, the statement regretted "detentions and fines of mostly opposition-affiliated campaigners" during the campaign.