The "special relationship" is of huge importance to London, particularly now as it prepares to sever its ties with the EU
The pair reaffirmed the "very special" relationship between their two countries, while May emphasised their "long history of shared values" and of standing together "when it counts the most", her office said.
Congratulating Trump on his shock win in Tuesday's presidential election, the British Conservative leader emphasised her wish to strengthen trade and investment as Britain leaves the European Union.
Trump, whose mother was Scottish and who has two Scottish golf courses, emphasised his close and personal connections and "warmth" for Britain, saying it is "a very, very special place for me and for our country".
The so-called "special relationship" is of huge importance to London, particularly now as it prepares to sever its ties with the EU following the June vote to leave the bloc.
May was quick to congratulate Trump in a letter, and some commentators had begun questioning why she had not yet received a phone call more than 24 hours after he won the vote.
"Mrs May and the rest of the government should be deeply concerned that the next leader of the world's most powerful country is not exactly falling over himself to make contact," one commentator wrote in The Daily Telegraph newspaper.
Finance minister Philip Hammond said the apparent delay in the phone call, initiated by Trump, was only because the two leaders "do not have any urgent business that we need to transact".
Trump was elected after one of the most bitter and divisive campaigns in history. May noted his commitment in his acceptance speech to unite his country, adding that it was a "task we all need to focus on globally".