In a speech in the lobby of one of his own New York towers Mr Trump told cheering supporters that he would be "the greatest jobs president that God ever created," and would revive America's international dominance.

"When was the last time anybody saw us beating, let's say, China in a trade deal? They kill us. I beat China all the time, all the time," he said.

The speech was supposed to be about 10 minutes in length but Mr Trump went on, largely off the cuff, for 45 minutes, according to a CNN report.

Mr Trump has long flirted with such a run but never formally announced before. He generally cites his wealth as his key qualification for the job.

"I'm the most successful person ever to run for the presidency, by far. Nobody's ever been more successful than me. I'm the most successful person ever to run … I have a Gucci store that's worth more than Romney," he told the Des Moines Register earlier this month.

Some suggest that his flirtation with a campaign in 2012, and this year's formal announcement is nothing but a publicity stunt for his TV show, another season of which is to air next year.

But even if that is the case his candidacy could cause serious disruption for the Republican Party.

With an estimated fortune of over $US4 billion ($5.17 billion), (according to Forbes) or nearly $9 billion ($11.62 billion), according to Trump, he can easily fund his own campaign, and his near universal name recognition he can soak up media attention that might go to other candidates.

This means it is possible that he will appear in early debates, which host Fox News has declared will only be open to the ten leading candidates.

According to the current Real Clear Politics Poll average, this could see Mr Trump on stage in the absence of several significant contenders, including Rick Santorum, Senator Lindsay Graham, Governor Bobby Jindal and Governor John Kasich. Other recent polls have at times even put him ahead of senators Marco Rubio and Rand Paul.

"I don't think when they limited it to ten [candidates] they ever imagined this could happen," said the director of the University of Virginia's Centre for Politics, Professor Larry Sabato, said if they want to prevent that from happening, other candidates - or their associated political action committees - are going to have to respond to the threat posed by Mr Trump. Given his wealth that could be an expensive exercise.

In the past Mr Trump has donated to the Democratic Party, but early in Barack Obama's term he became a cheerleader for "birther" conspiracy theories, holding that Mr Obama is not an American citizen.

He also subscribes to non-partisan conspiracy theories, arguing that climate change is hoax perpetrated by China and that vaccines cause autism.

He claims to know a quick method of defeating ISIS but is unwilling to share the idea lest it be stolen.

The Wisdom of Donald Trump

• "I'm the most successful person ever to run for the presidency, by far. Nobody's ever been more successful than me. I'm the most successful person ever to run. Ross Perot isn't successful like me. Romney — I have a Gucci store that's worth more than Romney." Interview with the Des Moines Register
• "I have an absolute way of defeating ISIS, and it would be decisive and quick and it would be very beautiful. Very surgical. "If I tell you right now, everyone else is going to say: "Wow, what a great idea." You're going to have 10 candidates going to use it and they're going to forget where it came from. Which is me." Interview with the Des Moines Register
• Donald Trump's gems on Twitter ...

Where’s the electability? Jeb is losing to HRC by 13 points. A Bush will never beat a Clinton. Wake up @GOP!— Donald J. Trump (@realDonaldTrump) December 30, 2014

I cannot believe how bad Jeb Bush looks with his insane answer on Iraq, and then his numerous corrections which made him look even worse.— Donald J. Trump (@realDonaldTrump) May 15, 2015

The concept of global warming was created by and for the Chinese in order to make U.S. manufacturing non-competitive.— Donald J. Trump (@realDonaldTrump) November 6, 2012

I am being proven right about massive vaccinations—the doctors lied. Save our children & their future.— Donald J. Trump (@realDonaldTrump) September 3, 2014

Ebola patient will be brought to the U.S. in a few days - now I know for sure that our leaders are incompetent. KEEP THEM OUT OF HERE!— Donald J. Trump (@realDonaldTrump) August 1, 2014