Conservative Lech Kaczynski will be the new Polish president, consolidating his Law and Justice party's narrow win in parliamentary elections last month.
Exit polls suggest Lech Kaczynski will be Poland's next leader
With 91% of votes counted, he had polled 55%, compared to 45% for his liberal rival Donald Tusk.
Mr Tusk has already admitted: "Today, I must tell myself I did not make it."
Mr Kaczynski said his opponent fought "a splendid battle" and called on Mr Tusk's Civic Platform to conclude talks on a forming parliamentary coalition.
Turnout was 50.49%, slightly higher than the first round a fortnight ago, when Mr Tusk was narrowly ahead.
Mr Kaczynski, whose identical twin Jaroslaw heads the Law and Justice party, has been advocating a "moral renewal" and a return to Christian values.
The BBC's Adam Easton, in Warsaw, says the result leaves the Law and Justice party holding the two top jobs in the country.
Both Mr Kaczynski and Mr Tusk are former activists of the Solidarity trade union, which led the country away from Communism.
A run-off was needed after neither achieved the required 50% majority needed for outright victory in the first round.
Mr Tusk's campaign spoke of the "great opportunity" offered by Poland's entry to the European Union last year.
But Mr Kaczynski focused his attacks on the outgoing government of ex-communists, accusing it of corruption and calling for "moral change". He also promised to maintain social welfare benefits for the poor.
The current president, former communist Aleksander Kwasniewski, is unable to stand again, having served the maximum two five-year terms permitted.
Under Poland's constitution, the president has less power than the country's prime minister, but retains a significant say in foreign policy.