Mr Bush, who served as the 41st US president between 1989 and 1993, died late on Friday at the age of 94.
Sully the dog will be travelling with the casket on the flight from Texas to Washington DC on Monday.
Mr Bush's body is due to lie in state this week ahead of a day of national mourning.
The coffin is being flown from Texas to DC on board Air Force One - temporarily renamed Special Air Mission 41, in homage to the late president - and then back on Wednesday, with Sully accompanying the body throughout.
