In a cabinet meeting, he said the move would trigger "very large" additional sanctions to be announced on Tuesday.
Mr Trump blamed the country's nuclear programme, and support for what he called international acts of terrorism.
While announcing the decision, the US president said it "should have happened a long time ago".
Mr Trump said that North Korea had "repeatedly supported international acts of terrorism" and added that the regime must act lawfully and also cease its nuclear weapons programme.
North Korean leader Kim Jong-un continues to pursue nuclear weapons and missile programmes in defiance of UN Security Council sanctions.
Mr Kim has made no secret of Pyongyang's plans to develop a missile capable of reaching the US mainland.
Last month, US Defence Secretary James Mattis said that the threat of nuclear attack from North Korea is increasing.
Monday's announcement comes after the president returned from an extensive tour of Asia last week.
Photo: AFP US President Donald Trump declared North Korea a state sponsor of terrorism.