The President said America would work with Britain to ensure political, economic and military prosperity post-Brexit.
Mrs May said a trade deal was being worked on between the two nations that would make commerce "quicker and easier" when Britain exits the Brussels bloc.
The Prime Minister said: "We are discussing how we can establish trade negotiations and lay the groundwork for UK/US agreements and see how we can work together.
"It's improtant for the prosperity of both of our nations."
Donald Trump said Brexit was "a sign of things to come" and "Brexit is going to be a wonderful thing for Britain".
He said: "You will have your own identity and you will be able to negotiate your own trade deals. Getting approvals from the group of European nations was very, very tough.
"But Brexit will be a fantastic and wonderful thing for Britain."
Theresa May and Donald Trump have held their first face to face meeting in the White House
Donald Trump has vowed to work with Theresa May by establishing trade deals
Mrs May was asked where she disagreed with US President Donald Trump and how he reacted to it.
She said: "There will be times when we disagree butI'm clear there are many issues on which the UK and United States stand alongside each other.
"We are in agreement on several areas where we can build an even stronger special relationship."
President Trump reaffirmed his belief that waterboarding works and added that he was remaining neutral with regard to Vladimir Putin, saying he "didn't know the gentlemen".
He vowed to represent his people "very forcefully" and said he would happily tackle Islamic State terror alongside Mr Putin's troops.
Theresa May jetted in to America yesterday to speak at the Congressional Republican Retreat.
Donald Trump hosted Mrs May at the White House today and it is thought the pair have thrashed out a post-Brexit trade deal.
Her speech, which reaffirmed the "special relationship" between Britain and America, was greeted with a standing ovation.
The Prime Minister outlined her plans for Britain to further its role as a world leader post-Brexit, she said the UK would work with America to crush Islamic State extremism and Mrs May also issued a warning over America's relationship with Russia.
She said President Trump should "beware" Vladimir Putin but should not shy away from "engaging with him frm a position of strength".
More to follow…