Poles will be able to cast their ballots at a polling station or choose to vote by mail.
The presidential election had been scheduled for Sunday, May 10, but failed to go ahead amid the coronavirus pandemic, which has claimed 839 lives in Poland.
The date of a new election is to be announced by Parliamentary Speaker Elżbieta Witek.
In total, 244 deputies voted on Tuesday in favour of a bill allowing a change in election rules, while 137 were against and 77 abstained.
The new system is intended to replace rules under which presidential elections would have been held by postal vote only amid the COVID-19 epidemic.
State news agency PAP reported that, under the latest plans, voters who aim to cast a postal ballot will have to notify officials at least 12 days before election day.
The deadline for people in quarantine amid the COVID-19 outbreak will be two days before the election.
Poles abroad who want to cast a postal ballot will have to inform a consul at least 12 days before election day.