"It is with a sense of relief that we are able to confirm that Patrick's body has been recovered and we will be able to bring him home soon," the post says.
The family of the hiker, who went missing in northern Mexico, says that the state government has informed them that he was killed by a criminal organization.
A statement from the family of Braxton-Andrew thanked Chihuahua state authorities for aiding in the search.
Thursday's statement says "authorities are searching for those responsible to bring them to justice."
Braxton-Andrew taught Spanish at Woodlawn School in Mooresville, North Carolina.
A page set up for him says he "died doing what he loved - traveling and meeting people."
Braxton-Andrew was last seen alive by hotel staff on Oct. 28 in Urique, a former mining village at the base of one of the many canyons that make up Mexico's Copper Canyon National Park.