In February, attackers mounted a bomb, grenade and gun assault on the main prison in Sanaa in which 29 inmates, including 19 jailed for terrorism-related crimes, escaped.
The 15-minute video, dated March 2014 and posted on a website used by extremists, shows masked men waving al-Qaeda's black flag and celebrating the arrival of the freed prisoners.
Its authenticity could not be independently verified.
"The Crusader enemy, dear brothers, still possesses cards which he moves around. We have to remember that we are always fighting the biggest enemy," says a man speaking in the open in a mountainous area, whom the video identifies as its leader Nasser al-Wuhaishi.
"We have to remove the cross, (and) the bearer of the cross, America," said Wuhaishi, who appeared with his face uncovered, wearing a T-shirt and sporting a dagger common among Yemeni men.
The video, entitled "Images from the reception of the freed prisoners from Sanaa's central prison," included testimony from fighters involved in the jailbreak.
"We planned that we would need 10 hand grenades," said a man identified as Munir al-Bouni.
Another man said: "Once you got out, you turned right and the guys were waiting."
A US State Department spokeswoman said in response to the video that it was "in no way breaking news that AQAP is a significant threat to the United States, the people of Yemen, to other people in the region and around the world."
Since 2009, the group had made several attempts to attack the United States and had carried out a number of attacks inside Yemen, Marie Harf told a regular briefing.
NTJ/NJF