Family friends on the flight will include George H.W. Bush's former chief of staff Jean Becker and Secretary of State James Baker.
A caption alongside the original Instagram post on Sully's official account read "Mission complete" as the dog prepares to go back to VetDogs to be re-homed with the Walter Reed National Military Medical Centre's Facility Dog Programme which helps other veterans.
That was a time that saw the end of the Cold War as well as the United States' routing of Iraqi President Saddam Hussein's army in the 1991 Gulf War.
The 41st USA president died Friday at age 94, at his home in Houston - "a very gentle and peaceful passing", his lifelong friend and advisor James Baker said Sunday on ABC's "This Week". Bush's presidential library have released.
The White House announced on Saturday that Trump and first lady Melania Trump will attend Wednesday's service at the National Cathedral.
There seems to be a taboo in the direct aftermaths of the death of great national figures like George H.W. Bush and John McCain to not "speak ill of the dead" and to instead eulogize their accomplishments as eminent men of politics.
Bush Jnr spoke of the joy the service dog, called Sully, brought his father late in life and how much the family will miss him.
Trump has ordered the federal government to close on Wednesday and both the New York Stock Exchange and Nasdaq will be closed on Wednesday in observance. His death also reduces membership in the ex-presidents' club to four: Jimmy Carter, Bill Clinton, George W. Bush and Barack Obama.
Mr Bush was born in 1924 and was shot down in the Pacific during World War Two. He enlisted in the Navy on his 18th birthday.
Bush served two terms as vice president under fellow Republican President Ronald Reagan before his own stint in the Oval Office from 1989 to 1993.
Soon after he reached the height of his political popularity following the liberation of Kuwait, with public approval ratings that are the envy of today's politicians, the USA economy began to sour and voters began to believe that Bush, never a great communicator - something even he acknowledged - was out of touch with ordinary people.