North Korean citizens in Malaysia will also be allowed to return home, the statement said.
Kim Jong Nam, 45, the half-brother of North Korea's leader, was poisoned at Kuala Lumpur International Airport on February 13 in a brazen Cold War-style assassination using a lethal nerve agent banned by the UN as a weapon of mass destruction.
"... following the completion of the autopsy on the deceased and receipt of a letter from his family requesting the remains be returned to North Korea, the coroner has approved the release of the body," said Najib.
Najib also announced that nine Malaysians barred from leaving North Korea after diplomatic ties worsened "have now been allowed to return to Malaysia".
"They took off from Pyongyang today at 7:45 pm Malaysian time, and will land in Kuala Lumpur tomorrow around 5am," he said in the statement which did not mention Kim Jong-Nam by name, referring to hims only as "the deceased".
"I had a deep personal concern about this matter, and we worked intensively behind the scenes to achieve this successful outcome. Many challenges were overcome to ensure the return of our fellow Malaysians. The safety and security of our citizens will always be my first priority," he said.
South Korea has blamed Pyongyang for Kim's death, but the North has rejected those claims and has never confirmed the identity of the victim, who was carrying a passport bearing the name of Kim Chol when he was attacked.
Pyongyang had denounced Malaysia's investigation as an attempt to smear the secretive regime, insisting that Kim most likely died of a heart attack.
The killing triggered a bitter row between Malaysia and North Korea, which have expelled each other's ambassadors and barred their citizens from leaving.
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)