Mr Trump took to the stage to speak to supporters at his New York headquarters, and said he had taken a call from Mrs Clinton, who will not be speaking publicly this evening.
“She congratulated us and I congratulated her on a very very hard fought campaign. We owe her a major debt of gratitude to for her service to our country,” he said.
Mr Trump said his pledge “to every citizen of our land” was to “be President for all Americans”.
“Now it’s time for America to bind the wounds of division,” he said.
“It is time for us to come together as one united people.”
Clinton campaign chairman John Podesta earlier told a room full of her supporters in New York that she would not be speaking tonight.
“You should get some sleep. We’ll have more to say tomorrow,” he said.
The shock result came after opinion polls over the weekend showed Mrs Clinton went into polling day with the advantage over her Republican rival.
The GOP are also predicted to hold onto a majority in the House and gain control of the Senate.
Clinton supporters in shock
North America correspondent Stephanie March is at Hillary Clinton’s headquarters in New York where supporters are visibly devastated.
“Hillary Clinton and her supporters had hoped to make history today by electing the first female president in the United States,” she said.
“Heading into election day polls had pointed to a victory for the Democrats nominee but losses key states south eastern of in Florida and North Carolina significantly narrowed her path to victory.”
Washington bureau chief Zoe Daniel is also at the headquarters:
“People have literally sat around in this venue on the floor, staring into space, some people are in tears. People are hugging each other,” Ms Daniel said.
“There’s just a sense of pervasive shock. Not only that Hillary Clinton appears to have lost the election, but that it has been such a complete and utter rout”.
Mrs Clinton had a lead in Florida of one percentage point and a win there would likely have secured her the presidency.