The billionaire businessman, who had been leading Cruz in recent Iowa polls, congratulated his rivals at a post-caucus event.
"We finished second, and I want to tell you something...I'm just honored. I'm really honored," Trump told a crowd of supporters. "I want to congratulate Ted and I want to congratulate all of the incredible candidates including Mike Huckabee, who's become a really good friend of mine. Congratulations to everybody."
It's a change in tone from his 2013 tweet:
"No one remembers who came in second." - Walter Hagen— Donald J. Trump (@realDonaldTrump) December 30, 2013
With nearly all of the GOP vote in, Trump won 24 percent of the vote, Cruz came in first with 28 percent of the vote and Rubio closely trailed Trump with 23 percent of the vote.
Trump said he's heading to New Hampshire Tuesday afternoon to prepare for the first-in-the-nation primary next Tuesday. He has consistently led the GOP presidential field in Granite State polls.
"We will go on to get the Republican nomination, and we will go on to beat Hillary or Bernie or whoever the hell they throw up there," said Trump, who added that he loves Iowa so much, he is considering purchasing a farm there.
Rubio, a senator from Florida, was the first of the three leading GOP candidates to speak publicly about the results.
"Tonight the people in Iowa have sent a clear message: After seven years of Barack Obama we are not waiting to take out country back," the Florida senator told his supporters.
He also professed confidence that he would secure the nomination in July.
"When I'm our nominee, we will unite our party, we will grow our party and we will defeat Hillary Clinton or Bernie Sanders or whoever they nominate," he said.