By Agence France-Presse
The declaration, long sought by the US, will be seen as a crucial step in the fast diplomatic dance on and around the Korean peninsula.
It comes less than a week before Kim meets South Korean leader Moon Jae-in for a summit in the Demilitarized Zone that divides the peninsula, and ahead of a much-anticipated encounter with US President Donald Trump.
"As the development of nuclear weapons has been verified, it is not necessary for us to conduct any more nuclear tests or test launches of mid- and long range missiles or ICBMs," Kim told a ruling party meeting.
"The northern nuclear test site has completed its mission," he added at the gathering of the central committee of the Workers' Party, according to the official KCNA news agency.
Pyongyang has made rapid technological progress in its weapons programmes under Kim, which has seen it subjected to increasingly strict sanctions by the UN Security Council, US, EU, South Korea and others.
For years the impoverished North has pursued a "byungjin" policy of "simultaneous development" of both the military and the economy, but Kim said that as it was now a powerful state, "the whole party and the whole nation should now focus on the development of the socialist economy".
"This is the party's new strategic policy line," KCNA cited him as saying.
Last year it carried out its sixth nuclear test, by far its most powerful to date, and launched missiles capable of reaching mainland United States.
Kim and Trump traded threats of war and personal insults as tensions ramped up, and even when there was an extended pause in testing, US officials said that it could not be interpreted as a halt without an explicit statement from Pyongyang.
South Korean envoys have previously cited Kim as promising no more tests, but Saturday's news is the first such announcement directly by Pyongyang.
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".
The formal declaration comes after Kim stated in his New Year speech that the development of the state nuclear force had been completed.
In the same address he said he had a nuclear button on his desk, prompting Trump to tweet that he had a bigger one of his own.
Events have moved rapidly since then, catalysed by the Winter Olympics in the South, and Seoul is now pushing for a peace treaty to formally end the Korean War, raising hopes that a settlement could finally be reached on the peninsula.
But there is a long way to go and Moon himself acknowledged this week that the "devil is in the details".