Tusk, of the Civil Platform party, has been the frontrunner, but conservative Kaczynski, of the Law and Justice party, made gains in the past few days.
The run-off is necessary, as neither man achieved the required 50 percent of the vote in national elections last month.
Under Poland's constitution, the president has less power than the country's prime minister, but has a significant say in foreign policy.
The outgoing communist President Aleksander Kwasniewski cannot run again, having served the maximum two five-year terms permitted.
Celebrity Couples of 2014 [PHOTOS]