The North has poured huge resources into the rebuilding of Samjiyon, the closest town to the dormant volcano that straddles the border with China.
The project is on a vast scale and includes a museum of revolutionary activities, a winter sports training complex, processing plants for blueberries and potatoes, and 10,000 apartments.
Kim is closely associated with the scheme and has visited the area several times, reportedly riding a white horse to the mountain's summit in October.
Kim had "worked heart and soul to turn Samjiyon County, the sacred place of the revolution, into the utopia town under socialism", the North's official KCNA news agency said.
The North is subject to multiple sets of international sanctions imposed over its nuclear and ballistic missile programmes and KCNA portrayed Samjiyon as a demonstration of resilience.
The Korean people were, it said, "advancing along the straight road chosen by themselves without any vacillation despite the worst trials".
The opening comes with nuclear negotiations with the US deadlocked since the Hanoi summit broke up in February.
Pyongyang has set Washington an end-of-year deadline to offer it new concessions, and has issued a series of increasingly assertive comments in recent weeks as time runs out.
KCNA released a a picture of Kim -- in a black leather trenchcoat and surrounded by fur-hatted officials -- cutting a red ribbon at an inaugural ceremony, with a statue of his father Kim Jong Il in the background.
According to North Korean propaganda the elder Kim was born at the nearby Mount Paektu Secret Camp where his own father Kim Il Sung was fighting the Japanese -- although independent historians and Soviet records say he was actually born in Russia, where the North's founder was in exile.
The official story plays a central role in Pyongyang's teachings about the Kim family, who have led the country for three generations, and every year 100,000 students and workers or more are taken on study trips to the area.
The scale of the Samjiyon project is immense: thousands of workers swarmed over the site during construction, AFP saw, many of them soldiers. Much of the North's army is devoted to construction.
Students have been sent to work on the scheme during university holidays, KCNA reported previously, while diplomats say children have also been deployed.