"The presidential election in the Czech Republic, our neighbouring country, ended today. General Petr Pavel has been elected new president!," Duda wrote on Twitter on Saturday.
"Mr President, sincere congratulations and greetings from Poland! We invite you to visit Warsaw," the Polish president said.
Petr Pavel, a retired army general, defeated billionaire Andrej Babis in a runoff vote on Saturday to become the Czech Republic's new president.
"President Andrzej Duda held a telephone conversation with Petr Pavel and invited him to pay an official visit to Poland," PAP was told on Saturday by Marcin Przydacz, the Head of the Presidential Bureau of International Politics.
"This was a short... very good conversation held in a good atmosphere. The presidents assured themselves of their commitment to good neighbourly Polish-Czech relations," Przydacz said.
Mateusz Morawiecki, the Polish prime minister, also congratulated the newly-elected president on his victory.
"Let me congratulate Petr Pavel on his election victory. Polish-Czech partnership is a safeguard of the security of our region. Being together we can achieve a lot," Morawiecki wrote on Twitter.
With all the ballots counted by the Czech Statistics Office, Pavel, a former army chief and high NATO official, had 58.3 percent of the vote compared with 42.7 percent for Babis. Turnout was just over 70 percent, a record high for a presidential vote. (PAP)