North Korea's Korean Central News Agency said it launched the destroyer - the second it built in 2025 - off the east coast of the country on Thursday.
KCNA cited Kim as saying the country's two destroyers would play a big role in improving the North Korean navy's operational capabilities.
Kim reiterated previous claims that his naval build-up was a justified response to perceived threats posed by the United States and its allies in Asia, which in recent years have expanded their combined military exercises and updated their deterrence strategies to counter Kim's nuclear ambitions.
He said the North would respond to the threats by his rivals with "overwhelming military action" and vowed to build a navy with "long-range operational capabilities".
In May, North Korea said the ship was damaged in a failed launch, sparking fury from Kim, who has vowed to build a stronger navy to cope what he calls escalating US-led threats against his country.
Kim earlier said the failed launch was caused by criminal negligence.
North Korea's state media later said that authorities detained four officials including the vice director of the Workers' Party's munitions industry department over the botched launch.
North Korea's extremely secretive nature makes it virtually impossible to independently confirm its announcement on the ship's repair.
Outside experts earlier said it remained unclear how severely the 5000-tonne-class destroyer was damaged and questioned North Korea's announcement that it could repair the ship's damage at an early date.
The damaged warship was North Korea's second known destroyer and seen as a crucial asset toward Kim's goal of modernising its naval forces.
It was in the same class as the country's first destroyer unveiled in April, which experts assessed as the North's largest and most advanced warship to date.
Kim lavishly praised that ship, which was launched in the western port of Nampo, saying it advances his goal of expanding the military's operations range and nuclear strike capabilities.
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