The Bush family spokesman tweets a picture of the yellow labrador retriever with the caption "Mission complete. #Remembering41".
The Bush family spokesman, Jim McGrath, posted the picture of the yellow labrador retriever called Sully HW Bush on Twitter with the caption: "Mission complete. #Remembering41."
He will reportedly be travelling with the former president's casket on his flight to Washington DC on Monday.
Mr Bush received Sully in June, after his wife Barbara Bush died, from America's VetDogs non-profit organisation.
The former president and Second World War veteran, who died on Friday aged 94, had a form of Parkinson's disease, and Sully could open doors, pick up items, summon help for him and even answer the phone.
Sully is named after Chesley B "Sully" Sullenberger III, the pilot who landed a damaged passenger plane on the Hudson River in 2009, saving all 155 passengers and crew.
The faithful canine will return to America's VetDogs in New York before joining the Water Reed National Military Medical Centre's Facility Dog Programme to help other veterans.
Mr Bush's son, George W Bush, posted the picture of Sully with the casket and said: "As much as our family is going to miss this dog, we're comforted to know he'll bring the same joy to his new home, Walter Reed, that he brought to 41."
When Sully went to work for Mr Bush in June, his spokesman said: "As one person said, he can do just about anything except make you a martini, but not to worry, he can go get you someone to make you a martini."
Americans will begin saying goodbye to Mr Bush on Monday when his body arrives in Washington for public viewing in the Capitol Rotunda.
The viewing will mark the start of four days of events that will include a state funeral at Washington's National Cathedral on Wednesday and a private service at Mr Bush's church in Houston on Thursday.