The Korean Central News Agency said Friday the 67-year-old former senior general was a traitor "for all ages."
Before being suddenly ousted this week as part of what appeared to be power consolidation by Kim, Jang had been vice chairman of the powerful National Defense Commission and secretary of the Workers' Party of Korea.
There were reports of executions of three of Jang's associates, leading analysts to say the purges may be part of an effort by the unpredictable Kim to consolidate his power. Kim became leader of the isolated communist country after the death of his father, Kim Jong Il, in December 2011.
The fast-moving developments in the highly secretive country raised concerns of its neighbors who have been troubled by North Korean actions that included defiance of U.N. sanctions by conducting nuclear tests and testing long-range missiles.
A U.S. State Department official said the execution of Jang, if confirmed, would be "another example of the extreme brutality of the North Korean regime."
Earlier, responding to Jang's ouster, China, North Korea's closest ally, said it wanted the North "to have national stability, economic growth and for its people to enjoy happiness."
The KCNA said Jang "is a traitor to the nation for all ages who perpetrated anti-party, counter-revolutionary factional acts in a bid to overthrow the leadership of our party and state and the socialist system." Jang also had been accused of challenging the "sole leadership system" and leading "a dissolute and depraved life."
Voice of America said the fate of Jang's wife, Kim Kyong Hui, was not immediately known. She is sister of the late leader Kim Jong Il and had been described as a major influence on the current leader.
South Korea's Yonhap News Agency said the Seoul government, already on the alert for North Korean provocations, expressed deep concerns over Jang's surprise execution and its implications for North Korea's future and its nuclear program. The report said few South Korean experts had expected the young Kim would take the extreme step of putting his uncle to death.
"The government has deep concerns about a recent series of developments in North Korea and is watching the situation closely," said spokesman Kim Eyi-do with the South Korean Unification Ministry after a meeting of security ministers. The Unification Ministry handles inter-Korean issues.
Yonhap said Jang had been considered a moderate in a regime full of hawkish military generals and an advocate of economic reform. South Korean experts did not rule out more executions by the Kim regime.
South Korea's military said it has stepped up surveillance on Pyongyang and remains vigilant about any provocations, although no special movement in the North had been noticed, Yonhap said.
"The Joint Chiefs of Staff has heightened readiness as the North Korean military started winter training earlier this month," a senior military official said. "We have beefed up military readiness and enhanced the system to closely monitor the North's moves."
Some sources said Jang's execution may indicate Kim's grip on power may not be as strong as earlier understood. This could lead to the North indulging in military provocations to increase internal unity, Yonhap said.
"This is a stunning development," Marcus Noland, a senior fellow at the Peterson Institute for International Economics, told CNN. "I've been following North Korea for 20 years and I do not remember them ever publicly announcing the execution of a senior leader." He said it appeared the regime is trying to intimidate anyone who might have independent ideas or be entertaining any ambitions.
John Park at Harvard's Kennedy School of Government told CNN Kim appears to have removed all of the old guard close to his father and to be bringing in his own inner group.
The Washington Post said although not much is known about Kim Jong Un analysts say he has been able to firm up his power faster than his father or grandfather. Purges in the country are not uncommon, but the Post said executions have mostly been of lower-level officials.
"We are in absolutely uncharted territory," Andrei Lankov, an expert on North Korean affairs at Seoul's Kookmin University, told the Post. "Kim Jong Un has changed the rules of the game. He's willing to purge the leaders closest to him, and quite publicly."
Lankov said Kim seems to be "far more ruthless than his father" and is "more inclined to kill." He also seems "more impulsive and emotional."
The Post quoted other analysts and some U.S. and South Korean officials as saying the North's behavior has become more reckless as was seen earlier this year with threats of nuclear strikes against its neighbors and the United States.
"I don't see any particular guile in what he's doing," said Victor Cha, a former White House director of Asian affairs. "He's doing what dictators do, especially somebody young and inexperienced. He's taking reckless action and doing things that are self-indulgent."