"Tonight is a victory for courageous conservatives," he declared, to great applause, as he railed against Washington, lobbyists and the media.
He took 28% of the Republican vote, beating his rival, the once frontrunner Donald Trump, and Marco Rubio.
Votes in the Democratic race are still being counted, and suggest a tight race between the two leading candidates.
With 85% of results in, frontrunner Hillary Clinton and self-proclaimed Democratic socialist Bernie Sanders are less than 1% apart.
Mr Trump congratulated the Texas senator and said he was "honoured" by the second-place finish.
At least two candidates are dropping out following the results.
Sources close to Democrat Martin O'Malley, former Maryland governor, have told the BBC that he will suspend his campaign - narrowing the field to two competitive candidates.
On the Republican side, Former Arkansas Governor Mike Huckabee tweeted that he too would suspend his campaign.
Iowa has an unusual election system called a caucus, which involves people gathering at private homes, schools and other public buildings across the state.
Democratic voters divide themselves into groups based on their preferred candidate, but the Republican caucus process is more like a traditional ballot.
Over the coming months, the other 49 states as well as US territories will vote for the party nominees.
Each states' delegates will be tallied and a nominee will become apparent as the summer draws near.
In November, the US will pick who its next president will be. He or she will assume office in January 2017.
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