The President made the declaration on Monday, saying the decision would impose further penalties on the secretive nation.
Mr Trump said the move was part of his ‘maximum pressure campaign’ against Pyongyang.
Trump told a cabinet meeting: ‘In addition to threatening the world by nuclear devastation, North Korea has repeatedly supported acts of international terrorism including assassinations on foreign soil.’
The country was removed from the list of countries viewed by the U.S. as state sponsors of terror in 2008 in an attempt to secure a deal to curb its nuclear weapons programme.
North Korea joins the likes of Iran, Sudan and Syria on the list.
The move comes after Pyongyang called Mr Trump ‘depraved and stupid guy’.
The attack came in North Korea’s state-run newspaper Minju Joson, which said the US will regret letting Mr Trump occupy the Oval Office.
It said he had ‘insulted the state and social system of the DPRK and the life of its people’.
The newspaper criticised Mr Trump’s recent visit to South Korea, in which he had some harsh words for North Korea and its leader, Kim Jong-un.
It wrote: ‘A load of rubbish spouted by the old lunatic Trump during his recent visit to South Korea was a total of all nonsense and paradox.
Most popular on Yahoo News UK
Gaia Pope death ‘not being treated as murder’ as three people arrested are released without charge
World’s longest aircraft the ‘Flying Bum’ seriously damaged after it crashes AGAIN
Here’s how to see messages someone has ‘deleted’ on WhatsApp
Fugitive taunts police by posting sightseeing pictures on Facebook while on the run
The Queen and Duke of Edinburgh’s 70 years of marriage in pictures
‘He insulted state and social system of the DPRK and the life of its people. This thrice-cursed crime can never be pardoned.
‘Trump had better pay heed to to the despicable plight of his country, the dark empire of evils under worldwide criticism, before poking his nose into others’ things.’
The statement came a day after North Korea said it would continue its nuclear weapons programme as long as the US and South Korea engaged in joint military exercises.
During his visit to South Korea, Mr Trump had a warning for Kim Jong-un and his regime.
He said: ‘Do not underestimate us. And do not try us. We will defend our common security, our shared prosperity, and our sacred liberty.’
Earlier this month, North Korea called Mr Trump a ‘nuclear war maniac’.
State news agency KCNA said the US president ‘needs medicine to cure his physical disorder’.