"I also loved to hear him explain his passion for this country - it was a true love that knew no petty boundaries or party lines", said Schwarzenegger in his message.
The moving tribute to the 41st USA president has been widely shared across social media, with the original post attracting more than 230,000 likes. More details are yet to come from the Bush family.
Thousands of mourners had flocked to Bush's presidential library on the campus of Texas A&M university, where they paid respects at a candlelit vigil at a nearby pond or contributing to growing flower memorials in Houston.
He died at his home in Houston on Friday at the age of 94 - the longest living president in U.S. history.
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Bush was also responsible for appointing Schwarzenegger chairman of the President's Council on Physical Fitness and Sports. Bush this morning and offer his condolences on behalf of himself, the first lady, and the entire country".
The pair were the second father and son to both serve as USA president, and the younger Bush spoke about the special moment they shared in the Oval Office after his inauguration in 2001. Trump and the first lady, Melania Trump, are scheduled to attend.
In honor of the 41st president, President Trump has declared Wednesday a national day of mourning, the White House said, and issued an executive order to close federal offices. Dozens of foreign leaders and United States luminaries are expected.
Vice-President Mike Pence said there was a "kindness about the man that was evident to everyone who met him".
Colorful socks were one of the former president's favorite fashion accessories.
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Le premier Ballon d'Or féminin a été attribué à la Norvégienne Ada Hegerberg , qui évolue sous les couleurs de l'OL. Hegerberg est primée alors qu'elle n'avait jamais été élu meilleure joueuse de l'année par la FIFA.
The former president had struggled for years with Parkinson's disease, which left him wheelchair-bound and repeatedly hospitalized - including after Barbara's death. "And the contrast between George H.W. Bush and the current president could not be more stark".
Bush's last words were to his son. "He was just one of the smartest people I've ever been around, and so down to earth", said Woods, who played a number of rounds with Bush while in Houston and at the exclusive Lochinvar Golf Club, just a short distance from George Bush Intercontinental Airport. A state funeral is being arranged with all of the accompanying support and honors.
On Wednesday, December 5th, Bush's funeral services will take place starting at 11 a.m. ET at the Washington National Cathedral in Washington, D.C.
Mr Bush will lie in state in the rotunda until his funeral on Wednesday, a day of national mourning.
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Bush's service dog, Sully , lying in front of the flag-dropped coffin of his owner has won the hearts of thousands. Lewis and Sons Funeral Home during the first departure ceremony for the State Funeral of president George H.W.
In 1799, the nation officially had its first state funeral with the death of George Washington, the first president.