Paul announced his candidacy on Tuesday in a post on his website, a few hours before what his political action committee described as "a very special rally" scheduled for a hotel in Louisville, Kentucky's largest city.
"I am running for president to return our country to the principles of liberty and limited government," he said in the post.
But the anti-war agitator who mounted a 13-hour filibuster to call attention to the United States' use of drones recently proposed a boost to military spending. The firebrand who wants to scale back the authority of the Federal Reserve has been quietly courting Wall Street donors.
And the 52-year-old former eye surgeon who harnessed the anti-establishment energy of the Tea Party movement has been raising money for fellow Republicans, at times upsetting the grassroots activists who have made him a national figure.
Tuesday's announcement makes Paul the second major Republican figure to announce presidential ambitions for 2016, after Senator Ted Cruz of Texas. A crowded field is expected, and candidates will be competing hard for constituencies ranging from the Christian right to traditional Wall Street Republicans.
On many issues, Paul does not differ from mainstream Republicans. He opposes Obamacare and abortion, and favors cutting taxes and spending. But his criticism of the Federal Reserve has spooked many in the party's business-friendly wing, and his proposal to balance the federal budget within five years is dramatic even by the standards of his anti-spending party.
Still, he has surprised many party insiders as he has laid the groundwork for the campaign.
"The people that I know of that talked to Rand Paul walk away pretty impressed," said Ron Kaufman, a former Mitt Romney adviser who now backs former Florida Governor Jeb Bush.
But Paul is being watched closely by the libertarian activists who were galvanized by the 2008 and 2012 White House bids of his father, former Congressman Ron Paul of Texas.
In Iowa, some prominent Ron Paul supporters have said they would back Cruz in 2016.
In New Hampshire, some libertarians have been dismayed by Paul's support of mainstream Republican Scott Brown in their state's primary for a U.S. Senate seat last year.
"There's an expectation that I'm supposed to be firmly in Rand Paul's camp, but I've got my reservations," said Aaron Day, a libertarian activist who heads the Republican Liberty Caucus of New Hampshire.
Paul was active in libertarian circles before he decided to run for an open U.S. Senate seat in Kentucky in 2009. He became one of the best-known faces of the insurgent Tea Party movement when he upset a favored candidate in the Republican primary a year later and went on to win the election.
TIED FOR FOURTH PLACE
Paul starts the campaign in the second tier of Republican candidates, drawing the support of 8.4 percent of Republicans, according to a March Reuters/Ipsos tracking poll.
That puts him behind Bush, who is considered a top contender among Republicans although he has not declared himself a presidential candidate; Wisconsin Governor Scott Walker; and former Arkansas Governor Mike Huckabee. He is in a statistical tie with four other candidates - Cruz, New Jersey Governor Chris Christie, neurosurgeon Ben Carson and U.S. Senator Marco Rubio of Florida.
Many of Paul's small-government notions, once consigned to the fringe, are becoming more broadly accepted among U.S. voters. He has sponsored legislation with two Democrats to loosen federal marijuana laws at a time when almost half the U.S. states have legalized the drug for medicinal purposes and several have made it legal for recreational use. Other Republican candidates now say states should have the right to set their own policies.
Paul has worked to build common ground with racial minorities who view the justice system as too punitive and technology-industry entrepreneurs who are skeptical of government regulation.
As Paul works to raise the $50 million or so he will need to be competitive, he can count on support from some of the more ideologically driven donors who underwrite the advocacy groups backed by billionaires Charles and David Koch.
"He's doing really well with those people who are not mainstream Republicans," said Frayda Levy, who sits on the boards of small-government advocacy groups Americans for Prosperity and Club for Growth.