Trzaskowski, the candidate of the opposition Civic Platform party, won the backing of 112,207 Poles in Britain, or 77.77 percent of the vote.
His rival, conservative incumbent Andrzej Duda, won 32,067, or 22.23 percent, PAP reported.
Amid the coronavirus pandemic, voting in Britain took place only by mail-in vote only.
Trzaskowski also won the most votes among Poles living in the UK in the first round.
According to final results announced by electoral officials on Monday evening, Duda won Sunday's presidential runoff election and secured another five-year term in office, with 51.03 percent of the vote overall.
Trzaskowski, the mayor of Warsaw, gained 48.97 percent overall, the National Electoral Commission (PKW) said.
In the first round of voting in the presidential ballot on June 28, no candidate won an outright majority, meaning a second round had to be held.
(pk)
Source: PAP