Separately, New Mexico Governor Bill Richardson, speaking on Wednesday after meeting North Korean diplomats in Santa Fe, said Pyongyang was sending "good signals."
Kim, who died on Tuesday aged 85, was awarded the 2000 Nobel Peace Prize for brokering the same year the first summit between the leaders of the rival Koreas.
North Korea's KCNA news agency said leader Kim Jong-il had approved the August 21-22 visit, headed by close aide Kim Ki Nam, secretary of the Central Committee of the ruling Workers' Party.
The delegation for the state funeral on August 23 will be the first high-level visit to the South by North Korean officials in almost two years.
Kim Jong-il had earlier sent a message of condolence to the former president's family, praising his efforts to reunite the two Koreas, divided since the end of World War Two.
Ties between the rival Koreas have headed back into the freezer since conservative President Lee Myung-bak took power in the South 18 months ago, cutting off aid to the North until it renounces nuclear weapons.
The decision to send the delegation is the latest in a series of conciliatory steps which follow months of military grandstanding by North Korea, including a nuclear test in May, that have deepened the impoverished state's isolation from the outside world.
They come as Philip Goldberg, the U.S. coordinator for the U.N. resolution aimed at North Korea's nuclear and missile tests, is in Singapore at the start of an Asian tour to strengthen the measures.
Hope for Thaw
The first sign of a more conciliatory North Korea came earlier this month when it released two jailed American journalists following a visit to Pyongyang by former U.S. President Bill Clinton.
New Mexico Governor Richardson, who met representatives from the North Korean mission to the United Nations, said Pyongyang hoped the Clinton visit would lead to a thaw in relations with the United States.
"The North Koreans are sending good signals, that they're ready to talk directly to the United States," Richardson said on CNN. "They felt that the President Clinton visit was good, that it helped thaw relations, make them easier."
"I detected for the first time ... a lessening of tension, some positive vibration," he said.
Clinton was the most senior U.S. envoy in nearly a decade to travel to Pyongyang and meet Kim Jong-il.
Richardson said the North Koreans had indicated that they felt the decision to pardon the journalists had been a "gesture on their part" and that they were now owed a gesture by the United States.
He said the North Koreans, who had requested the meeting, had indicated they wanted to have a dialogue with the United States though Washington wants Pyongyang to return to six-party talks to discuss the denuclearization of the Korean peninsula.
North Korean leader Kim also this month met the head of South Korea's powerful Hyundai Group, a major investor in the North.
That meeting helped win the release of a Hyundai worker detained since March and agreement to resume tourism to the North and reunions of families separated by the 1950-53 Korean War.
Adding to the flurry of diplomatic activity around the prickly North, one leading South Korean daily reported that China's chief nuclear envoy had ended a three-day visit to Pyongyang.
It gave no details of the visit by Wu Dawei but as the North's only major ally, China is one of the few global powers with much influence over Pyongayang.
