Mr Trump made the announcement after historic talks with North Korean leader Kim Jong-un in Singapore - the first such talks between the two countries.
And on Wednesday, the official newspaper of the Workers' Party of Korea featured three full pages of photos from Kim's summit with Trump. The president had announced a halt in the drills after his meeting with Kim on Tuesday.
Trump is celebrating Tuesday's agreement to launch a process to denuclearize the Korean Peninsula, though experts and allies are still awaiting details on the broad accord the two sides say they've reached. The Korean War ended in 1953 without a peace treaty, leaving the two sides in a technical state of war.
The US President said: "Just landed - a long trip, but everybody can now feel much safer than the day I took office".
Trump said he also agreed to destroy a missile engine test site.
Trump vowed to rain down "fire and fury" on Pyongyang if it threatened the USA, but instead in Singapore it was compliments that flowed, as the United States leader described Kim as "talented" and said they had forged a "special bond".
North Korea typically heavily censors its local and foreign content, with events often not being reported until several days after, if at all.
Earlier Wednesday, Trump wrote online that North Korea no longer poses a nuclear threat to the USA after his meeting this week in Singapore with Kim, adding that Americans should "sleep well tonight".
Former U.S. ambassador Bill Richardson told VOA he is concerned about no verification of what the North Koreans will do about missile technology in their country, no details of nuclear reduction or the peace treaty ending the Korean War from the early 1950s, and human rights.
For his part, Kim also thanked them for helping North Korea have a successful meeting with the United States, the report said.
Last year Kim was "Little Rocket Man", according to Trump, and US officials regularly mentioned his likely role in the assassination of his half-brother with nerve agent in a Malaysian airport, as well as his uncle's execution.
When relations between the USA and the DPRK thawed slightly between 1990 and 2005, a repatriation agreement allowed 229 sets of remains to come home to American families.
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Trump's claim that North Korea no longer poses a nuclear threat is questionable considering Pyongyang's significant weapons arsenal.
Moon has championed engagement with the North, and the agreement's language on North Korea's nuclear program was similar to what the leaders of North and South Korea came up with at their own summit in April. A year ago it tested long-range missiles that could reach the USA mainland, although it remains unclear if it has mastered the technology to deliver a nuclear warhead that could re-enter the atmosphere and hit its target.
"People are going to be very impressed and people are going to be very happy and we are going to take care of a very risky problem for the world", Trump said.
North Korea also was no longer the United States' "biggest and most risky problem", he added. "No longer - sleep well tonight!"
South Koreans applauded in a train station as they watched; the South Korean president grinned broadly; one official compared the summit, favourably, to the birth of his daughter.
But it did also make nuclear war all but inconceivable at the present moment.
President Trump and Chairman Kim Jong Un conducted a comprehensive, in-depth, and honest exchange of opinions on the issues related to the establishment of new U.S. -DPRK relations and the building of a lasting and robust peace regime on the Korean Peninsula. He told reporters that if the USA concludes they no longer are, the freeze "will no longer be in effect". Responding to questions, he said "absolutely" he would invite Kim to the White House.
President Donald Trump is thanking North Korean leader Kim Jong Un for "taking the first bold step toward a bright new future for his people", saying their summit Tuesday "proves that real change is possible!"
Japan's Prime Minister Shinzo Abe spoke to Donald Trump after the summit, saying there was "great meaning in Chairman Kim's clearly confirming to President Trump the complete denuclearisation". Pompeo, the former Central Intelligence Agency director, then plans to fly to Beijing to update the Chinese government on the talks.
In Japan, the prospect of cancelled US-South Korean drills was met with concern.
Also, the US forces stationed at South Korea admitted that Department of Defense or the Indo-Pacific Command had given them "no updated guidance on the execution or cessation of training exercises" and hence will continue to coordinate with their Seoul counterparts and maintain their current positions until further notice.
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