Although the two Republican presidents were in many ways polar opposites - the soft-spoken, patrician Bush reportedly once dismissed the blustering New Yorker as a "blowhard" and even voted for his rival Hillary Clinton - President Trump paid the late leader a gracious tribute, saying he had "inspired generations of his fellow Americans to public service".
Mr Bush's body is due to lie in state this week ahead of a day of national mourning.
The former president passed away on Friday at the age of 94.
"And he cocked one eye open and quipped, 'Well, you better hurry", James Baker recalled today as he described the 41st president's final hours of life.
Mr Jimmy Carter, now the oldest surviving former USA president, said Mr Bush's administration "was marked by grace, civility and social conscience".
He will be buried at the presidential library in Texas, alongside his wife, Barbara Bush, who died seven months ago. Bush hadn't left his bed in the past three or four days and also hadn't been eating. "We all began to think, 'Here we are".
Sully, the service dog of the late President George H.W. Bush, has been pictured lying beside his former owner's coffin.
¿Por qué Carola de Moras "desapareció" de la clausura de la Teletón?
El cierre de la Teletón iba según lo presupuestado y Don Francisco iba llamando al escenario a los distintos animadores para continuar con el show.
During his later years, Bush suffered from a condition that mimics Parkinson's disease, which didn't allow him to walk and made it hard for him to speak.
"By the time he got back here to Houston from his summer in Kennebunkport, I think he was pretty much ready to go. It was my privilege to have worked with him on an array of world-changing policy achievements", Mulroney said, listing German re-unification and NAFTA as examples.
Still, when an aide told Bush his friend was visiting that day, "he perked up". 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 2½ years.
After it became clear that death was imminent, they got all the Bush kids on the phone, with son Neil Bush the only one in the room.
"George H.W. Bush's exemplary service and deep commitment to his country informed everything he accomplished over his decades in public life", Trudeau tweeted from the sidelines of the G20 Summit in Buenos Aires, Argentina, on Saturday morning.
Bush's son Jeb, Governor of Florida, retweeted the photo, with the simple words: "Sully has the watch". "He looked at me, he said, 'Bake, where are we going today?' I said, 'Well, Jefe, I said we're going to heaven.' He said, 'Good, that's where I want to go'".
Speaking to the media, America's VetDogs said Sully will stay at their NY headquarters over the festive season and then undergo physical and occupational therapy.