Polish President Bronislaw Komorowski has conceded the election to conservative challenger Andrzej Duda (photo) following the release of exit polls, the BBC informs.
They suggested Mr Duda had taken the run-off vote by 53% to 47%.
Mr Duda had edged Mr Komorowski, who had been the favourite, in the first round but did not gain the 50% needed to win outright.
The president has limited powers, but is head of the armed forces and can veto new laws.
The exit polls had been delayed after a woman died at a polling station on Sunday.
Official results are expected later on Monday.
“I respect your choice,” Mr Komorowski told voters at a gathering of his supporters. “I wish my challenger a successful presidency.”
Speaking to supporters in Warsaw, Mr Duda said: “Thank you President Bronislaw Komorowski for the rivalry of this presidential campaign and for your congratulations.
The victory will be a wake-up call to Prime Minister Ewa Kopacz, an ally of Mr Komorowski, ahead of parliamentary elections this autumn.