"I'm running for president and I hope to earn your support!" he tweeted. In an early preview of his campaign message, he says in an accompanying video that "it is going to take a new generation of courageous conservatives to make America great again."
Several other Republicans are expected to enter the race in the coming weeks, including former Florida Gov. Jeb Bush, Wisconsin Gov. Scott Walker and two Senate colleagues, Kentucky's Rand Paul and Florida's Marco Rubio.
Cruz, 44, is the son of an American mother and Cuban-born father and would be the nation's first Hispanic president.
He has considerable appeal among the Republican Party's base of conservative and small-government, low-tax tea party voters. After his election to the Senate in 2012, the former Texas solicitor general quickly established himself as an uncompromising conservative willing to take on Democrats and fellow Republicans alike.
Criticized by members of his own party at times, he won praise from ultraconservative tea party activists in 2013 for leading a 16-day government shutdown in an unsuccessful drive to repeal President Barack Obama's health care overhaul.
Recent Republican history, however, could work against Cruz and other deeply conservative candidates as they battle through state-by-state primaries and caucuses. That selection process is dominated by the most conservative Republican voters and can lead to the nomination of a candidate who is not acceptable to more moderate Republicans and independent voters.
Cruz is set to release a book this summer that he has said would reflect themes of his White House campaign. In a recent Associated Press interview, he said he wants to counter the "caricatures" of the right as "stupid," ''evil" or "crazy."
"The image created in the mainstream media does not comply with the facts," said Cruz, who does not believe in climate change.
The senator was born in Canada, but two lawyers who represented presidents from both parties at the Supreme Court recently wrote in the Harvard Law Review that Cruz meets the constitutional requirement to run.
Cruz had hinted openly at his interest in seeking the White House for months, and his intention to jump into the race was confirmed Sunday by a strategist for the first-term senator, who spoke to The Associated Press on condition of anonymity so as not to preclude the formal announcement.
Details about Cruz's Monday campaign launch were first reported by The Houston Chronicle.
Cruz is scheduled to give the convocation at Liberty University, a private Christian college, in Virginia on Monday. He has courted evangelicals and other social conservatives as part of an attempt to build a coalition of conservatives frustrated with Republican elders in Washington.
Cruz continues to be a leading voice for repeal of the Affordable Care Act, widely known as Obamacare. He promises to abolish the tax-collecting Internal Revenue Service, scrap the Education Department and curtail federal regulators, likening them to locusts.
He also is a staunch social conservative who opposes both gay marriage and abortion rights. His father, Rafael, is an outspoken evangelical pastor.
On foreign policy, Cruz was among 47 Republican senators who signed a letter to Iran's supreme leader warning that any nuclear deal that is struck with the Obama administration and five other world powers could become null and void after the 2016 election when the current president leaves the White House. Cruz is a strong backer of Israel.
He also is opposed to Obama's executive action to ease deportations of millions of immigrants in the country illegally and to the White House opening to communist Cuba, his father's homeland.
Associated Press writer Steve Peoples contributed to this report.
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