Mrs May’s response was released in a statement by Downing Street around 90 minutes after Mr Trump made his speech accepting victory over Hillary Clinton.
The Prime Minister said on Tuesday that she aims to speak with the president-elect “at the earliest possible opportunity” to discuss the “special relationship” between the US and the UK.
In her statement, Mrs May said: “I would like to congratulate Donald Trump on being elected the next president of the United States, following a hard-fought campaign.
“Britain and the United States have an enduring and special relationship based on the values of freedom, democracy and enterprise.
“We are, and will remain, strong and close partners on trade, security and defence.