Polish President Bronislaw Komorowski has conceded the election to conservative challenger Andrzej Duda following the release of exit polls, BBC News reports.
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.