"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."
Donald Trump is actually running for president. Few people expected it to happen - he's gone through the motions many times before - and his political rants up until now have been roundly derided as a joke. But this time he actually said the words, and he seems like he means it.
With campaign staff in key early voting states and a net worth he puts at more than $8.5bn, he has the resources to roil the Republican presidential field.
Mr Trump is polling high enough to get a spot on the stage in the forthcoming Republican debates, and he's already proven a willingness to take swings at his opponents. Jeb Bush and Marco Rubio "don't have a clue", he said in his announcement speech. "How are these people going to lead us?" he asked.
If he says that enough times during a debate - or in a multi-million dollar television advertising spree - a lot of people are going to stop laughing and take notice. And that's probably just what Mr Trump wants.
Mr Trump expressed support for gun rights and said he would protect US government programmes like Medicare, Medicaid and Social Security.
And he said he would "immediately terminate" President Barack Obama's executive order on immigration, which would save undocumented migrants from deportation.
"Sadly, the American Dream is dead", Mr Trump said.
"If I get elected president I will bring it back bigger and better and strong than ever before. We will make America great again."
He becomes the 12th Republican to declare, with Wisconsin Governor Scott Walker and Florida's former governor Jeb Bush among the early frontrunners.
