The move puts Mr Kim at the head of North Korea's vast armed forcesNew North Korean leader Kim Jong-un has been hailed by state media as "supreme commander" of the country's powerful armed forces for the first time.
The ruling party newspaper Rodong Shinmun also called on Kim Jong-un to lead North Korea to "eternal victory".
State media had been calling Mr Kim "the great successor" after the death of his father Kim Jong-il on Monday.
Mr Kim has little political experience and experts believe senior officials are guiding the transition.
"We declare from our hearts ... we will complete the task of songun (military-first) revolution under comrade Kim Jong-un", the paper said in an editorial.
The "songun" policy prioritises spending on North Korea's armed forces.
Last year, the Swiss-educated Mr Kim was made a four-star general and given senior positions in the government and the Workers' Party.
The announcement comes on the 20th anniversary of the declaration of the late Kim Jong-Il as supreme commander in 1991.
Large crowds have continued to mourn Mr Kim's death in the capital Pyongyang, gathering to bow in front of large portraits of him set up around the city.
Some mourners were reported to be volunteering to clear snow from the streets in advance of the funeral motorcade that is expected to take Mr Kim's body around the city on Wednesday.
"Our general Kim Jong-il went on trips of field guidance for people throughout his whole life, on roads covered with snow, and how can we make his last trip on snow-covered roads?", mourner Jong Myong Hui told AP.
Pyongyang residents were quoted by the official Korean Central News Agency (KCNA) as expressing their appreciation for the state distribution of fish, an order reportedly issued by Kim Jong-il a day before his death.
"Salespeople and citizens burst out sobbing at fish shops in the capital", according to the Rodong Shinmun paper.
The South Korean government confirmed on Saturday that Lee Hee-ho, wife of late South Korean President Kim Dae-jung, will head a delegation to the North next week to express their condolences.
This will not however be an official visit and the South Korean government has issued a travel ban on its citizens in connection with the leader's death, the Yonhap news agency reports.
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