Abigail Ogle, an Oklahoma City local news anchor, tweeted: "Sully, the service dog of President George H.W. Bush, keeping watch over his best friend".
The public 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.
Bush's crowning achievement as president was assembling the worldwide military coalition that liberated the tiny, oil-rich nation of Kuwait from invading Iraq in 1991 in a war that lasted just 100 hours. Thousands of mourners paid respects at a weekend candlelight vigil at a nearby pond, and others contributed to growing flower memorials at Bush statues at both the library and a park in downtown Houston.
Captioned, "Mission complete" by Bush's former spokesman Jim McGrath, the photograph served as a heartbreaking farewell between Bush and Sully, who the former president began working with after his wife Barbara Bush died earlier this year. Trump directed the presidential plane - called Air Force One when the sitting President is aboard - to pick up Bush's casket and transport it to Washington.
Mr Bush's body is due to lie in state this week ahead of a day of national mourning.
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"President Bush was a dedicated and thoughtful leader who stuck by his convictions and values", Trudeau said.
One of Bush's major achievements was assembling the global military coalition that liberated the tiny, oil-rich nation of Kuwait from invading neighbour Iraq in 1991.
The former governor of California said in his touching tribute that he enjoyed sledding with Bush at Camp David, while praising the former president for inspiring America to join "our fitness crusade" by hosting the Great American Workout with him on the White House lawn.
A humble hero of World War II, Bush was just 20 when he survived being shot down during a bombing run over Japan.
Baker instead emphasised his friend's foreign-policy successes: navigating the end of the Cold War, negotiating two nuclear arms-reduction treaties, and summoning a varied global coalition to eject Iraqi troops from Kuwait in the first Gulf War.
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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.
Bush will be buried next to his wife Barbara, who died in April, and their daughter Robin, who died of leukemia at age three.
Bush turned his attention to politics in the 1960s, being elected to his first of two terms in Congress in 1967.
It wasn't only former political rivals Bush found easy to befriend.
Bush replied: "Good, that's where I want to go".
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"I'm a sock man", he told his granddaughter Jenna Bush Hager during a 2012 Today Show segment.
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