"I am running for president to return our country to the principles of liberty and limited government," Paul said on his campaign website.
Paul, a conservative libertarian who was elected to the Senate in 2010 with strong support from the Tea Party movement, was expected to make a more formal announcement later in the day.
He summoned supporters and reporters to a speech at 1600 GMT in Louisville, Kentucky, where he has served as senator since January 2011.
Jeb Bush, brother of former president George W. Bush, leads in opinion polls for the primary elections, although he has yet to officially announce his candidacy.
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On the Democratic side, Hillary Clinton has a team and campaign machine in place, suggesting she will announce in the coming weeks.
In recent days, Paul's team has left little doubt as to his presidential ambitions. A video released recently and hinting at a campaign slogan said: "One leader will stand up to defeat the Washington machine and unleash the American dream."
And it is by billing himself as a different kind of Republican leader that Paul will look both to rally ultra-conservatives during the primaries and then broaden the base of his party among young people, independents and minorities. It will be a true high wire act.
His father Ron Paul was a libertarian candidate for the presidency -- conservative on economic issues but liberal on social issues.
He has pushed against the surveillance programs of the National Security Agency and has promoted criminal justice reform to end mandatory jail term minimums, endearing himself with libertarians.
On foreign policy, he has long been in favour of US disengagement, going as far as proposing an end to all US foreign aid.