His eldest son, former President George W. Bush, and others from the family traveled on the flight from Houston.
President Bush's spokesman Jim McGrath shared a photo of Sully and the casket captioning it, "Mission complete".
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.
A statement was released from his office, it said: "George Herbert Walker Bush, World War II naval aviator, Texas oil pioneer, and 41st President of the United States of America, died on November 30, 2018".
Following the death of the former president at the weekend, Sully will move on to help the next person in need with George W. Bush confirming the details on Instagram.
Migrants march towards United States border in present of power
One of the other men who illegally crossed into the United States after traveling in the caravan has been deported in the past. Judge Jon Tigar rejected the Justice Department's request to suspend his earlier order temporarily blocking the ban.
A photo of George HW Bush's service dog lying downbeat besides the casket of his old master on Sunday has spread across social media, causing an outpouring of emotion.
He will be honoured during several private and public events in Houston and Washington before he is buried in Texas next to his wife, Barbara, and their young daughter Robin, who died in 1953.
The high point of the commemorations, planned with military precision by a Pentagon task force, will come Wednesday with a state funeral at Washington National Cathedral - the first presidential funeral since Gerald Ford died in 2006.
Trump has said he plans to designate Wednesday as a national day of mourning. He had joined the Navy when he turned 18. The couple was married for 73 years, longer than any other USA presidential couple. Bush enrolled at Yale University after military service, becoming a scholar-athlete and captaining the baseball team to two College World Series before graduating Phi Beta Kappa after just 2½ years. He was elected to the first of two terms in Congress in 1967. Sully will reportedly make one last journey with the 41st president, who served from 1989 to 1993.
Houston will host a public tribute to Bush on Monday night. He lost his bid for re-election to then-Arkansas Gov. Bill Clinton, who would later become a close friend. In particular, news commentators have also focused on the seemingly hallowed relationship Bush had with his late wife, Barbara Pierce Bush, further cementing his patriarchal legacy as a good politician, good father and good husband.