The First Armored Division's base in northwestern Sanaa, the capital of Yemen, will be turned into a national park, according to Hadi's decrees.
The country will now have seven military zones instead of five. The decree also restructures the military intelligence agency to allow for more than one body to oversee it.
Among the most prominent decisions was the creation of a Defense Reserve Force comprised of six brigades that will be based in Sanaa to protect Hadi's government from military coups and other disruptions, according to a senior military official who spoke anonymously because of the sensitivity of the subject.
The defense ministry will also have a new Inspector General.
Presidential spokesman Mahboub Ali told The Associated Press that the decrees were supposed to be announced last November, but international advisers from the United States, United Kingdom, Jordan and the U.N. were late in making proposals.
The decisions were announced while Saleh was in neighboring Saudi Arabia for medical treatment. He has been under international pressure to leave the country.
Last year Hadi ordered similar overhauls of the country's Defense Ministry. Wednesday's reshuffle removes the last of Saleh's closest relatives from their posts.
Saleh's family-owned TV channel Yemen el-Yowm reported Wednesday that the president's son "welcomes the decision" and "does not oppose it."
Similarly, al-Ahmar released a statement calling the decision "historical."
Yemen's military, deeply fractured and divided, faces powerful tribes needed to help fight al-Qaida. There have been accusations that Saleh's supporters turned a blind eye when al-Qaida overran cities in southern Yemen during the 2011 uprising to create an atmosphere of chaos and delay any transition.
The deputy leader of al-Qaida in Yemen, Saeed al-Shihri, harshly criticized Yemen's neighbor to the north, Saudi Arabia, for its policy of allowing the United States to launch deadly drone strikes from bases in the kingdom. This followed an al-Qaida claim that al-Shihri was not killed in a drone strike, as Yemen reported.
The audio recording was released Wednesday. It was not known when it was made.