Mr Trump, a Republican, has never run for the party's nomination before, but has often talked about it.
"I am officially running for president of the United States and we are going to make our country great again," he told supporters at New York's Trump Towers on Fifth Avenue.
He said his fortune would allow him to be an effective president.
"Our country is in serious trouble. We don't have victories anymore," he said.
"When was the last time anyone saw us beating, let's say, China in a trade deal?
"They kill us. I beat China all the time."
