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"This is a movement. But we have to go all the way. I am so proud to be your nominee for president," he told delegates by video link.
The New York billionaire, who has never previously held public office, said it had been "a very special day" to watch his adult children declare New York's delegate count that put him over the top.
"What we did getting the party's nomination, I will never forget it," he said. "With your vote today, this stage of the presidential process has come to a close. Together we have achieved historic results."
Trump will address the convention in person on Thursday when he will formally accept the nomination and promised to outline "how we build a brighter and more hopeful future for all Americans."
"We are going to win the presidency and bring real change and leadership back to Washington," he said to applause. "We will win in November."
He praised his pick for vice president, Indiana Governor Mike Pence, as an "incredible man" who would make "a great vice president."
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