It was not immediately known when the new rules would come into force.
During a meeting with Trump in New York last month, Polish President Andrzej Duda said that Poles had been waiting for such a move for 30 years.
At the time, Trump said the United States expected to be able to make Poland part of its Visa Waiver Program “over the next couple of months.”
Poland, a staunch ally of the United states, has long been pressing Washington to lift visas, which are seen by many Poles as a humiliating encumbrance.
Citizens of countries which are part of the Visa Waiver Program can travel to the United States for business or tourism for up to 90 days without a visa.
The threshold for a country to enter the program is a 3-percent refusal rate.
The rate for Polish nationals for the fiscal year ending September 30, 2018 was 3.99 percent, down from 5.92 percent a year earlier, according to the US embassy in Poland.
Meanwhile, in recent months a growing proportion of Polish applicants have been issued US visas, causing the denial rate to drop below 2.8 percent for the first time in history, Poland’s onet.pl news website reported in September.
Poland’s ruling conservatives are keen to strengthen their country’s military and business ties with the United States.
America will station around 1,000 extra troops in Poland under a declaration signed by the Polish and US presidents in June.