Mr Cruz made the announcement via Twitter shortly after midnight on Monday, local time.

I'm running for President and I hope to earn your support! pic.twitter.com/0UTqaIoytP — Ted Cruz (@tedcruz) March 23, 2015

He tweeted the announcement hours before he was expected to officially declare his run during a speech at Liberty University in Virginia.

Mr Cruz is a star among the Tea Party right of the GOP, who has made himself as famous for hounding his own party's establishment as for opposing Obama administration policies.

He delighted his supporters by forcing the government shutdown in 2013, widely seen as a tactical catastrophe for congressional Republicans, and backs populist conservative policies such as abolishing the Internal Revenue Service and stripping power from regulatory bodies such as the Environmental Protection Agency. He does not believe that human activity is causing climate change.

In a 2011 interview he described America's social security safety net for the elderly as Ponzi scheme and outlined a plan to reduce and privatise it.

Reflecting the views of some on the far right of American politics he has publicly mused about the threat of creeping Sharia law and said that he would like to the see the federal attorney general, Eric Holder, impeached.

But unlike other insurgents, his sometimes-radical positions do not appear to have ruled him out of contention for the nomination even though he is running ninth in polls of likely candidates. He is viewed as a brilliant debater and shrewd campaigner who has met with resounding success in both his legal and political careers.

He won his Senate seat in 2012 after defeating the Texas lieutenant governor, David Dewhurst, in a primary campaign in which he vowed to spend more than other candidates on building a wall on the state's border with Mexico.

During that campaign he ran advertisements boasting about the victory he won in the Supreme Court while he served as the Texas solicitor-general defending a controversial law making it easier to execute Mexican citizens convicted in Texas.

Cruz was born in Canada to an American mother and a Cuban emigre father. Born as a legal citizen though in a foreign country he remains eligible for the office of president.

In a 2012 he described to the New Yorker how he learnt both his debating skills and his political philosophy as a high school member of a group known as the Free Market Education Foundation, which introduced him to the writings of conservative economic philosophers such as Milton Friedman, Friedrich Hayek, Frederic Bastiat and Ludwig von Mises.

He travelled to Rotary Clubs competing with other teenagers in speech competitions and went on to become a champion debater at Princeton before studying law at Harvard and clerking with the conservative Supreme Court chief justice William Rehnquist.

Cruz's decision to make his candidacy speech at Liberty University in Virginia rather than in his home state is significant. Liberty University is a private Christian university founded by the evangelist Jerry Falwell. It appears Mr Cruz hopes to challenge establishment frontrunners by forging a coalition between the Republican Party's Christian social conservative base and its Tea Party wing.

During a speech at the recent Conservative Political Action Conference Senator Cruz dazzled the audience with a speech that attacked mainstream politics as a whole rather than the Democratic Party.

Pacing the stage like a preacher and speaking without notes or prompter he won a standing ovation from the young crowd. He urged them to demand that Republican candidates cite instances when they had acted on conservative issues such as support for Israel, opposition to abortion and illegal immigration.

"If you have a candidate who has stood up against Democrats, that's great. When have you been willing to stand against Republicans?"

The great divide in America was not between Republicans and Democrats, he said, but  "between career politicians in Washington and the American people".

This is the argument he is expected to make against the presumed frontrunner, Jeb Bush, brother and son of a president and a former governor of Florida.

Some of the other candidates in what will be a crowded Republican field are expected to announce next month, including Marco Rubio, a senator from Florida and Rand Paul, a senator from Kentucky, as is the Democratic frontrunner Hillary Clinton.