Democrats, meanwhile, are in a nail-biter fight with Hillary Clinton and Bernie Sanders tied.
With 98 percent of the GOP precincts in Iowa reporting, Cruz had 28% of the vote, Trump had 24%, Marco Rubio had 23%, Ben Carson had 9 percent, Rand Paul had 5%, Jeb Bush had 3%, Carly Fiorina, John Kasich, Mike Huckabee and Chris Christie each had 2%, and Rick Santorum had 1%.
With 95 percent of the Democratic precincts in Iowa reporting, Clinton and Sanders were tied at about 50%.
The victory for Cruz is the first time that the conventional laws of politics have applied to Trump, a billionaire businessman who has built his campaign around the perception that he's a winner who can bring his unique skills to the White House.
But Trump's big personality, social media presence and large rallies failed to overcome Cruz's more traditional approach to Iowa's retail politics. Cruz spent months touring the state and reaching out to evangelical voters.
The win sets Cruz up as a formidable contender in the delegate-rich, Southern states that crowd the GOP calendar in the coming weeks and offers movement conservatives hope that one of their own can become the nominee for the first time since Ronald Reagan.
But Trump said he's still confident he'll win the presidency.
"We will go on to get the Republican nomination and we will go on to easily beat Hillary or Bernie," Trump told supporters. "We finished second, and I have to say I am just honored."
Democratic and Republican casualties
The caucuses resulted in two casualties -- one on each side.
Former Maryland Gov. Martin O'Malley, a Democrat, and former Arkansas Gov. Mike Huckabee, a Republican, both dropped their candidacies after faring poorly.
Rubio thrilled with his showing
Republican Marco Rubio also had a strong night in Iowa, which could set him up as the best placed potential establishment candidate to take on "outsider" challengers Cruz and Trump.
"This is the moment they said would never happen. For months, they told us we had no chance," a jubilant Rubio said, as he became the first candidate to appear before the cameras to comment on the results.
"They told me that I needed to wait my turn, that I needed to wait in line. But tonight here in Iowa, the people of this great state have sent a very clear message --- after seven years of Barack Obama, we are not waiting any longer to take our country back."
Several candidates visited caucus sites on Monday evening. Trump mingled with voters at one West Des Moines location with his wife, Melania, and did some last minute campaigning.
"We are going to strengthen our borders, we are going to build a wall. We are going to bring our country back," Trump said, stirring cheers from some in the audience.
Long-shot candidate Carly Fiorina appeared at the back of the room at the same caucus site and waved to those inside. Cruz was also expected to head to a caucus location.
Several hundred thousand Iowans in 1,681 precincts are expected to venture out with scattered snow showers in the forecast to exercise their cherished right to cast the first votes in the race that will determine the 45th President of the United States.
The Iowa caucuses have huge symbolic power, and while they don't always predict who will be sworn in as the next president, they can offer a crucial boost to candidates who do well. They also spell doom for those who barely register and then do badly in the New Hampshire primary.
Even before the caucuses began, Carson's campaign said he wouldn't go directly to New Hampshire or South Carolina -- the site of the next primary contests. Instead, the retired neurosurgeon, who was briefly the Iowa front-runner last fall, will go to Florida to rest and see family.
Former Pennsylvania Sen. Rick Santorum is also skipping New Hampshire. He will go straight to South Carolina, which holds its Republican presidential primary on February 20.
Democrats are also in a nail-biter race.
Clinton expressed confidence about her prospects earlier Monday and reiterated her argument that Sanders won't be able to deliver on some of his ambitions policy proposals.
"I am a progressive who wants to make progress and actually produce real results in people's lives. That's what I'm offering," she said on CNN's "New Day." "I'm not overpromising."
The former secretary of state, and her husband, former President Bill Clinton, eased their nerves ahead of the caucuses with a walk around Gray's Lake in Des Moines, leaving staffers behind.
On the eve of the caucuses, the race to win Iowa turned more sharply combative as candidates desperate for an edge dashed through a frenzied final day of campaigning.
Trump branded Cruz a "liar" and made a play for the Texas senator's evangelical power base. Cruz questioned Trump's conservative authenticity on abortion and religious liberty and appeared alongside Duck Dynasty's Phil Robertson, who branded same-sex marriage "wicked" and "evil."
Sanders complained that he could not keep up with distortions of his record made by the Clinton camp. And a former aide to President Barack Obama took to Twitter to accuse the Vermont senator of repudiating their old boss' record.
Clinton is positioning herself as the most qualified commander in chief and the best person to save Obama's legacy. But Sanders is vowing to stage a "revolution" that will overturn a corrupt political structure bankrolled by a busted campaign finance system that he says is soft on Wall Street and favors the wealthy.