Trzaskowski represents the ruling Civic Coalition (KO), while Nawrocki is backed by the opposition Law and Justice (PiS) party.
Polling stations opened at 7 a.m. local time and are set to close at 9 p.m.
The outcome is seen as pivotal for the country's future direction.
Exit poll projections are expected shortly after voting ends, with official results due on Monday.
The winner will serve a five-year term as head of state, overseeing defence and foreign policy and holding veto power over legislation.
Trzaskowski narrowly edged Nawrocki in the first round of voting on May 18, winning 31.4 percent of the vote to Nawrocki's 29.5 percent.
Photo: Polish Radio
Incumbent President Andrzej Duda, in office since 2015, is barred by the constitution from seeking a third term. His second term ends on August 6.
A pre-election media blackout began on Saturday under which domestic outlets are prohibited from publishing opinion polls on candidate support.
The ban lasts until voting ends. Political campaigning is also forbidden during this period.
The National Electoral Commission (PKW) said nearly 29 million citizens were eligible to vote, including Polish expatriates at 511 overseas polling sites.
More than 700,000 Poles living abroad have registered to vote by absentee ballot, according to officials.
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Source: IAR, PAP/PAP