The three had released an earlier statement saying: "We would like to express our deep appreciation to the United States government, President Trump, Secretary [of State Mike] Pompeo and the people of the United States for bringing us home".
"It is a patriotic moment for many Americans to see these men returning to U.S. soil and walking in such good health".
Speaking with the former detainees by his side at Joint Base Andrews near Washington, Trump called it a "great honor" to welcome the men to the U.S.
The three men released this week were the last Americans being held in North Korea.
They are being sent to the Walter Reed Medical Center for additional medical testing, according to the White House.
"As everybody is aware, the past administration has always been asking for three hostages to be released from a North Korean Labor camp, but to no avail".
"Special night for these three really great people", Trump said.
"I think this will be a very big success". Trump also said he was optimistic that their upcoming talks would lead to improved relations between the countries.
"We think relationships are building with North Korea", Trump had said, adding: "We'll see how it all works out".
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In an impromptu chat before the media with Mr Trump, Kim Dong-chul said: "It's like a dream and we are very, very happy". Vice President Mike Pence, second lady Karen Pence, Pompeo and more than 200 members of the press were also on hand to witness their return.
Officials said that step removed the last major obstacle to the nuclear-focused summit, providing Trump with tangible evidence that his policy of engagement was reaping rewards.
Trump had previously suggested that the demilitarised zone between the two Koreas - the site of a recent summit between Kim and Moon - could also be an appropriate venue for his meeting with the North's leader.Other possible sites reportedly included Mongolia and Switzerland.
He was detained on similar charges, but it's not known if their cases were related.
On "Fox & Friends", Loesch pointed out that the New York Times bashed Secretary of State Mike Pompeo for not appearing with Trump when he pulled out of the Iran nuclear deal. USA news networks covered the meeting at around 3 AM local time.
Trump thanked the Korean leader for their release.
If it materializes, the Kim-Trump meeting will be the first time a sitting USA president has met with a North Korean leader. "All three men have been daily in our thoughts; and our hopes and prayers have been fulfilled by their release", the university said.