Poland's liberal opposition Civic Platform party has won a massive poll victory, ousting Prime Minister Jaroslaw Kaczynski's conservatives.
Donald Tusk said the election had helped restore hope among Poles
With 99% of votes counted, Donald Tusk's pro-EU party received more than 41% of the votes, while Mr Kaczynski's Law and Justice (PiS) got about 32%.
The election was called two years early after Mr Kaczynski's coalition collapsed over a corruption probe.
Mr Tusk is expected to hold talks with likely coalition partners this week.
An alliance with the centrist Polish Peasants' Party would give the Civic Platform a clear majority.
Civic Platform's total translates to 209 seats in the 460-seat lower house of parliament, the Sejm, with the Peasants Party on course to get 31 seats.
Mr Kaczynski has admitted defeat and congratulated his rival
Turnout was the highest recorded in Poland since communism fell in 1989.
The prime minister's twin brother, Lech Kaczynski, is Poland's president and does not face an election until 2010. But the opposition's win looks big enough for it to be able to override his veto power.
Mr Kaczynski said his party would be a "decisive, tough opposition"
PiS has pursued former communists and adopted a sceptical approach to the European Union, while Civic Platform has promised lower taxes and a more business-friendly administration with closer ties to Europe.
Civic Platform says it will repair Poland's strained ties with Germany and other EU neighbours. It also wants strong ties with the US but Mr Tusk has vowed to withdraw 900 Polish troops from the US-led coalition force in Iraq.
EU leaders hailed the result. European Commission President Jose Manuel Barroso said he expected "fruitful co-operation" with the new government.
Mr Tusk was showered with confetti as he appeared in front of cheering supporters at its campaign headquarters on Sunday evening.
"We went into this election in order to make everyone, without exception, feel good in their country, in their home," he said.
"I thank everyone who, in an impartial way, has helped restore hope among Poles."
Poles have become disillusioned with democracy following a succession of unhappy coalition governments, says the BBC's Adam Easton in Warsaw.
The country is polarised over the figure of Prime Minister Kaczynski, 58, who commands both strong support and deep opposition, says our correspondent.
He has given extra power to anti-corruption agencies and purged former communists, while promoting an assertive foreign policy and traditional Catholic values.