Domański said the government would issue the necessary regulations on Friday and estimated that pump prices could fall by about PLN 1.20-1.30 (around EUR 0.30, USD 1.15) per litre.
"Starting this weekend, prices at gas stations in Poland will be lower," Domański wrote in a social media post.
Prime Minister Donald Tusk also welcomed Nawrocki's decision, saying it meant motorists will be paying less for fuel.
"It wasn't me who won. The Polish people won because they will be paying less for fuel starting this weekend," he wrote on Facebook.
Nawrocki announced in a televised address on Thursday that he had signed the law but would refer it to the Constitutional Tribunal for a review of its constitutionality.
The president said he expected fuel prices to fall immediately and reach the levels promised by members of the governing coalition during the election campaign. He also argued that the government bore responsibility for fuel prices.
"Every zloty obtained thanks to this law must be spent on lowering fuel prices," Nawrocki said.
Domański criticised the president for delaying the law's signing, saying it could have been signed "many, many weeks" earlier to benefit consumers.
He said the government intended to extend its "Fuel Prices Down" programme at least through the end of the year.
The law was published in Poland's official Journal of Laws on Thursday evening, allowing the government to proceed with implementing regulations, state news agency PAP reported.
Government spokesman Adam Szłapka told broadcaster TVN24 that such regulations were ready and would be processed by the finance ministry on Friday.
The windfall tax is intended to help lower retail fuel prices, which have reached record levels amid the ongoing conflict in the Middle East.
The law applies to profits from the sale of liquid fuels earned between March 2026 and March 2027.
It marks the governing coalition's second attempt to introduce the tax. Nawrocki blocked an earlier version of the bill in August by referring it to the Constitutional Tribunal for a preventive review before it took effect.
The president has separately submitted his own bill to parliament that would allow temporary measures to reduce fuel prices, including limits on fuel companies' margins and a temporary exemption of fuel sales from the retail sales tax, according to the PAP news agency.
The president's decision drew mixed reactions from politicians.
Government coalition lawmakers said it showed that "pressure works," while opposition politicians called on the government to radically cut pump prices.
Interior Minister Marcin Kierwiński wrote on X that "fear of voters prevailed over political hatred."
Left-wing lawmaker Tomasz Trela said Nawrocki had signed the law because he had been "backed into a corner."
Presidential spokesman Rafał Leśkiewicz described the signing as "a victory of common sense over Prime Minister Donald Tusk's political calculations," adding that Nawrocki had acted "for Poles" rather than yielding to the government.
Opposition leader Jarosław Kaczyński wrote on X that Tusk "no longer has an alibi" and could not "shift responsibility" for fuel prices.
The far-right Confederation group criticised the legislation. Its leader Sławomir Mentzen said the windfall tax was unconstitutional and accused Nawrocki of giving in to "Tusk's propaganda."
Urszula Cieślak, an analyst at the Reflex fuel market consultancy, told the PAP news agency that gasoline could fall below PLN 7 per litre and diesel below PLN 8 following the president's decision.
She said the scale of the reductions would depend on whether the government also cuts VAT and excise taxes and introduces maximum prices, as it did under the first phase of its "Fuel Prices Down" programme, or uses the approach adopted in late August, when only VAT was cut and price caps were introduced.
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Source: IAR/PAP