Trump was introduced to supporters by Republican vice president-elect Mike Pence, who called it "a historic night."
"The American people have spoken and the American people have elected their new champion," Pence said. "And it’s almost hard for me to express the honor that I and my family feel that we will have the privilege to serve as your vice president of the United States."
Trump took the stage to deafening cheers from supporters gathered at the New York Hilton Midtown hotel.
"Thank you very much. Sorry to keep you waiting, complicated business," he said, explaining that he had just spoken on the phone with Hillary Clinton and accepted her concession.
He emphasized the need for unity, even though he'd said seconds before that Clinton had "congratulated us—it’s about us—on our victory."
Trump said that he congratulated Clinton on the "very very hard-fought" race.
"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," Trump said, to applause from the crowd. "I mean that very sincerely."
"Now it’s time for Americans to bind the wounds of divisions," he said. "It is time for us to come together as one united people."
Trump pledged to be a president for Republicans, Democrats and independents alike, adding that it was "important" to him.
"For those who have chosen not to support me in the past, of which there were a few people," he said, drawing laughter from the crowd, "I’m reaching out to you for your guidance and your help so that we can work together and unify our great country."
Trump described his campaign as a "movement made up of millions of hardworking men and women" of "all races, religions, backgrounds and beliefs."
He called for cooperation on "the urgent task of rebuilding our nation and renewing the American dream," citing his business record as the reason that he saw "tremendous potential" in America.
"It’s going to be a beautiful thing," Trump said.
He promised to rebuild infrastructure, care for veterans, strengthen the economy, and "get along with all other nations willing to get along with us."
"No dream is too big, no challenge is too great. Nothing we want for our future is beyond our reach," he said. "America will no longer settle for anything less than the best."
Trump said that under his leadership, the country "will deal fairly with everyone" despite putting its own interests first.
"We will seek common ground, not hostility; partnership, not conflict," he said.
Trump went on to thank his family and his political advisors, including former New York mayor Rudy Giuliani, Republican National Committee Chairman Reince Priebus, New Jersey Gov. Chris Christie (R), Ben Carson and former Arkansas Gov. Mike Huckabee (R).
In "two years or four years or maybe even eight years," Trump told the cheering crowd, "you will say that was something you were, really were very proud to do."