Downing Street sources said May had a phone call with Trump this afternoon, in which she congratulated him on his "hard-fought" campaign.
According to a statement, the pair agreed the US-UK relationship was "very important and very special", and building on it will be a priority.
President-elect Trump set out his close and personal connections with, and warmth for, the UK. He said he was confident that the special relationship would go from strength to strength.
The PM apparently also discussed expanding the UK's relationships around the world and "noted President-elect Trump’s commitment in his acceptance speech to uniting people across America, which she said is a task we all need to focus on globally".
“The Prime Minister said that we have a long history of shared values and added that she looked forward to that continuing in the future," they added.
“She highlighted her wish to strengthen bilateral trade and investment with the US as we leave the EU. But she said that our relationship is so much more than that and our two countries have always stood together as close allies when it counts the most. President-elect Trump strongly agreed and added that the UK is a ‘very, very special place for me and for our country’."
There have been suggestions May was snubbed by Trump, who called nine world leaders - including Irish Taoiseach Enda Kenny - before he picked up the phone to the British PM.
Trump reportedly invited Kenny to attend the St Patrick's Day celebrations at the White House - although St Paddy's day isn't until March. Hardly "asap", is it.
US election: What you need to know