Mrs May confirmed Mr Trump was "100% behind Nato" despite the president's recent comments calling the transatlantic alliance obsolete.
Both leaders said they would work to establish trade negotiation agreements.
Mrs May also said Mr Trump had accepted an invitation from the Queen for a state visit later this year.
"Great days lie ahead for our two peoples and our two countries," Mr Trump said.
The prime minister added that a trade agreement between the UK and US was "in the national interest in both our countries".