Jang was executed on Thursday shortly after a special military trial, KCNA reported.
He had been accused of a string of criminal acts including corruption, womanising and drug-taking.
It's this incredibly public condemnation of this once very powerful man.
Harry Fawcett, Al Jazeera correspondent
"The accused Jang brought together undesirable forces and formed a faction as the boss of a modern day factional group for a long time and thus committed such hideous crime as attempting to overthrow the state," KCNA said.
The sacking on Monday means Pyongyang is undergoing its biggest leadership upheaval since the death in 2011 of former leader Kim Jong-il, the younger Kim's father.
KCNA said Jang had been removed from all his posts and expelled from the Workers' Party.
Jang was married to Kim's aunt, the daughter of the North's founding leader Kim Il-sung, and was widely considered to be working to ensure his nephew firmly established his grip on power in the past two years.
Jang had been a prominent fixture in many of the reports and photographs of Kim Jong-un's public activities, but his appearances have tapered off sharply this year and he has not appeared in official media since early November.
Al Jazeera's Harry Fawcett, reporting from Bangkok, said the execution has laid bare a massive power struggle in the secretive country.
"It's this incredibly public condemnation of this once very powerful man," our correspondent said.