Trump pledged that he would be "president for all Americans" in his New York victory speech. He also praised his defeated rival for her years of public service.
"Hillary has worked very long and very hard over a long period of time, and we owe her a major debt of gratitude for her service to our country," he said.
"I pledge to every citizen of our land that I will be president for all of Americans."
He added: "It's been what they call a historic event - but to be a really historic we have to do a great job.
"I promise you I will not let you down, we will do a great job - I look very much forward to being your president.
"And hopefully at the end of two years, or three years, or four years - or maybe even eight years - you will say that so many of you worked so hard, but you will say that was something that you were really very proud to do."