Mr Trump said it was a "special night for these really great people" as they arrived at the Andrews Air Force Base near Washington.
"I think this will be a very big success".
He further said that a new relation has been forged between the U.S. and North Korea and added, "A year ago, one would say it was not possible".
"My proudest achievement will be - this is a part of it - will be when we denuclearize that entire peninsula", he said.
"We are happy for the hostages and their families", his parents, Fred and Cindy Warmbier, told The Washington Post on Wednesday. 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.
South Korean and USA officials announced in March that Trump, despite previously trading barbs with his North Korean counterpart, had agreed to meet with Kim by May to negotiate an end to North Korea's nuclear weapons program.
In what is viewed as an early diplomatic concession, Kim released three US prisoners held in North Korea.
Trump thanked the Korean leader for their release.
Face-to-face talks between Mr Trump and Mr Kim are set to take place within weeks, with a time and place to be made public in the coming days. More than a dozen abductees still remain missing, according to the Japanese government.
He had said he favoured holding the meeting at the Demilitarised Zone, the heavily fortified border separating the two Koreas.
In April, Mr Trump stunned the world by accepting an invitation to meet Mr Kim in an unprecedented sit-down.
It will be the first ever summit between the leaders of the two countries.
And Trump and North Korean dictator Kim Jong-Un are even planning a face-to-face summit at an as-yet-undetermined point in the future.
Leader Jason Day gets feet wet at Wells Fargo
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Asian Cup draw better this time, says Gurpreet
The UAE, as virtue of being the host, was top seeds placed in Group A along with India, Thailand and Bahrain. He believes that the sheer number of quality coaches in the ISL and I-League have helped the players.
Destiny 2's Warmind Expansion Drops Tomorrow
It means you'll be able to play all the Warmind and Curse of Osiris Crucible maps in public games. Right now, the Destiny 2 backend servers are down for maintenance, according to developer Bungie.