"We've now established that Kim Chol is Kim Jong-Nam," Inspector General Khalid Abu Bakar told a news conference, but he declined to give details of how the body's identity was confirmed.
"For the security of the witnesses so I'm not going to tell you how it was done," he said.
Malaysian authorities had earlier declined to officially confirm the victim's identity or release his body, saying they needed a DNA sample from next-of-kin.
The 45-year-old was carrying a passport bearing the name of Kim Chol when he was attacked on February 13 with the lethal nerve agent VX by two women.
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The brazen Cold War-style killing triggered a bitter diplomatic row between the previously friendly Asian nations, which have expelled each other's ambassador and refused to let their citizens leave.
North Korea has never confirmed the identity of the dead man, but has denounced the Malaysian investigation as an attempt to smear the secretive regime, insisting that he most likely died of a heart attack.
Pyongyang retaliated by formally expelling his Malaysian counterpart, who was already back in Kuala Lumpur for consultations.
Prime Minister Najib Razak on Friday urged Malaysians to pray for the safe return of nine compatriots barred from leaving North Korea.
Three Malaysian embassy staff and six family members remain stuck in Pyongyang after North Korea barred Malaysians from leaving the country on Tuesday, prompting a tit-for-tat move by Malaysia.
Two Malaysians working for the UN World Food Programme were permitted to leave North Korea on Thursday.