Within minutes of the report being issued, Trump tweeted: "This is very good news for North Korea and the World - big progress!"
UN Ambassador Nikki Haley welcomed the announcement and praised the UN Security Council for coming together to achieve this goal.
The country's state media reported that its leader, Kim Jong-Un, has suspended nuclear and long-range missile tests.
The surprise announcement by Pyongyang on Saturday to halt nuclear and missile tests and shut down its nuclear test site is expected to top the agendas, ministry officials said.
The formal declaration of an end to testing comes after Kim reiterated the North's nuclear status in his New Year speech and said he had a nuclear button on his desk - prompting Trump to tweet that he had a bigger one of his own.
He also says he's looking forward to his upcoming summit with North Korean leader Kim Jong Un.
The Prime Minister of Japan said what's important is that this development leads to complete, verifiable and irreversible dismantlement of North Korea's nuclear and missile programs.
"This is an action that was taken against weapons of mass destruction, and I think this gave a certain message to North Korea as well", defence minister Itsunori Onodera said.
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Her sisters are being super supportive of her ... her family is rallying around her . They're both there for their daughter. "This moment is all about love for her".
The two countries started talking again for the first time in two years via a special phone line, and those talks led to North Korea's participation in South Korea's Winter Olympics.
In an earlier statement released by his office, Guterres wished the two Koreas ahead of their April 27 summit "every success in their courageous and important task of resuming honest dialogue leading to sustainable peace on the Korean Peninsula".
Kim Dong-gil, the director of the Korean Peninsula Center at Peking University, says now that North Korea has nuclear weapons, he believes they will use them as a bargaining chip to officially end the 1950-53 Korean War, make arrangements to guarantee North Korea's safety and ultimately allow North Korea to open up its economy to the rest of the world.
The British government said in a statement that Pyongyang's commitment was a positive step and hoped it indicated "an effort to negotiate in good faith".
The party decided that nuclear and ICBM launches will cease as of Saturday - it has not carried any out since November - and the atomic test site at Punggye-ri "will be abolished". Kim has committed himself to the path of denuclearization and will now focus exclusively on economic growth and improving the national economy, the source said.
But Kim told the Workers' Party meeting: "A fresh climate of detente and peace is being created on the Korean peninsula and the region and dramatic changes are being made in the worldwide political landscape".
Kim extended an invitation to South Korea's leader to go to Pyongyang, and the two agreed to meet Friday at the heavily fortified DMZ.