The Polish team, comprising Karol Zalewski, Natalia Kaczmarek, Justyna Święty-Ersetic and Kajetan Duszyński, clinched their victory in a time of 3:09.87, setting a new European and Olympic record.
The Dominican Republic finished second ahead of the USA.
A number of top officials have expressed their congratulations to the Polish team, including Poland's Prime Minister Mateusz Morawiecki and President Andrzej Duda.
The Polish head of state wrote on his Twitter account: "Yes! The first gold medal for Poland at the Tokyo Olympics! (...) What a result! (...) Joy and pride!"
The 4x400m mixed relay is a new format at the Olympics, and it entails teams of four athletes - two women and two men - racing against each other.
With their Saturday victory in the mixed 4x400m relay, Poland's team secured the country's second medal at the Summer Olympics in Tokyo, Japan.
On Wednesday, the Polish women’s quadruple sculls team took the silver in the Olympic rowing competition.