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".
Although the UK cannot begin to negotiate trade deals until it leaves the EU, Mr Trump has said he wants a "quick" deal after that.
When asked about Mr Trump's scheduled phone call with Russian President Vladimir Putin on Saturday, the president played down any suggestion that he would lift US sanctions against the Kremlin.
"It's very early to be talking about that," he told reporters during a news conference.