About 155 million people of some 350 milllion eligible voters in the 25 member states cast their ballots, making it one of the biggest democratic exercises in the world.
Commentators have predicted that parties of the centre-right will maintain their position as the biggest single bloc in the new parliament.
The unprecedented apathy among voters had been feared by EU observers.
However, the BBC's Oana Lungescu in Brussels says few had predicted that turnout would be lowest not in the UK and the Netherlands, as five years ago, but in the eight central and eastern European countries that joined the EU on May 1.
Our correspondent says this is unusual, since after previous enlargements, new members showed greater enthusiasm about European polls than voters in the old member states.
"Regrettably, Europe is too absent from European elections in east and west," outgoing European Parliament President Pat Cox said.
However, Mr Cox put a brave face on the results, pointing out that more than 150 million people had taken part in Europe's biggest-ever elections.
He said eastern and central European countries had successfully mobilised large majorities to vote in favour of EU membership in referendums last year.
"Nothing like an equivalent effort of mobilisation was made on this occasion," he said. "I think a lot of public opinion felt, 'But we voted for that last year, why are you asking us again?'"
Latest results
Germany's governing Social Democrats recorded their worst result since World War II. Official results showed the party took just 21.5% of the vote, with the Christian Democrats set to be clear winners with 44.5%.
French President Jacques Chirac's Union for the Popular Movement, with 16.6% of the vote, finished a far second behind the Socialist Party, on 28.9%, according to the final results.
In Britain, Labour and the Conservatives both saw their vote slump. With most results in, the two main parties looked set to secure less than half of the vote between them, for the first time ever. The Tories had 27.4% and Labour 22.3%, while the eurosceptic UK Independence Party was running third with nearly 17%.
In Poland - largest of the new EU members - partial results indicated the governing left party won just 9% of the vote. Turnout there was just under 20%.
Italian Prime Minister Silvio Berlusconi suffered a setback with his centre-right coalition losing ground. His Forza Italia remained the most popular party, but saw its share of the vote drop to 21%, compared with 29.4% in the 2001 general elections.
In Spain, the ruling Socialists appear to have bucked the trend, winning some 43.7%, while the conservatives took about 40.8 %, according to provisional results.
With all the ballots counted in the Czech Republic, eurosceptic Civic Democrats won 30% of the vote to trounce the ruling Social Democrats who only managed to poll 8.8%.
The lowest turnout was in Slovakia, where fewer than 17% cast their votes. Prime Minister Mikulas Dzurinda's SDKU party led the polls with 17.09%, closely followed by the nationalist HZDS party of controversial ex-Prime Minister Vladimir Meciar on 17.04%.
Beach or ballot box
Voters in 19 of the 25 EU nations cast ballots on Sunday, the fourth day of elections which have already seen the other six countries complete polling for their share of the 732 MEPs.
Voters in Brussels tell us who they voted for in the European elections and why
Reports from across the continent said sunny weather drew people out of their homes - but not necessarily to the polling stations.
The Associated Press news agency reported from Athens that it seemed most Greeks preferred to spend the day on the beach, but the interior ministry said turnout had topped 60%.
The highest turnout is expected from the least populous EU member.
Malta, which only joined the EU on 1 May, saw more than 80% of its electorate vote, partial results indicate.
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