The Ipsos survey showed Trzaskowski with 50.3 percent of the vote, while his conservative rival, Karol Nawrocki, garnered 49.7 percent.
The pollster said its results could vary by up to 2 percentage points from the final official count.
The official results are expected on Monday.
"We won," Trzaskowski told supporters after the exit poll was released, while acknowledging that his lead—if confirmed—was "razor thin."
Rafał Trzaskowski with wife Małgorzata on election night. Photo: PAP/Paweł Supernak
He thanked voters and all those who backed him in the race, pledging to "connect and build" as the country’s new president.
"This is a special moment in Poland’s history, and I am convinced it will help us all move forward like a torpedo, to focus primarily on the future," he told the crowd.
"I will truly be the president of all Poles; I will be your president," he declared.
Nawrocki did not concede defeat, urging his supporters to wait for the official results.
Karol Nawrocki votes at a polling station in Warsaw on Sunday, accompanied by his family. Photo: PAP/Paweł Supernak
“We will win and save Poland," he vowed.
"We have to win tonight—and we know we will," he added, as updated projections and vote counts were expected later in the night.
If confirmed by the National Electoral Commission (PKW), Trzaskowski's win could bolster the pro-European government of Prime Minister Donald Tusk.
Trzaskowski, 53, a senior politician of Tusk's ruling Civic Coalition (KO), campaigned on a platform of strengthening Poland’s ties with the bloc and advancing judicial reforms.
Nawrocki, a conservative historian backed by the opposition Law and Justice (PiS) party, had pledged to veto liberal reforms, promote traditional Catholic values and align Poland more closely with Donald Trump's America.
The close race highlighted deep divisions in Polish society over the country’s direction, with the president holding significant veto power over legislation.
Trzaskowski’s win is expected to facilitate Tusk’s reform agenda, including efforts to reverse controversial judicial changes made by the previous government from 2015 to 2023.
The election saw high voter turnout, with 72.8 percent of eligible voters casting ballots, according to the exit poll, conducted for broadcasters TVP, TVN and Polsat.
In the first round of voting on May 18, no candidate won an outright majority, meaning a second round had to be held.
The Polish president is the head of state and has the power to veto legislation passed by parliament, a key prerogative in a country where traditionalists and liberals are bitterly divided.