Mr Bush, who served as the 41st United States president between 1989 and 1993, died late on Friday in Texas at the age of 94.
Bill Clinton will be among the living USA presidents to attend, along with dozens of foreign leaders including Germany's Angela Merkel.
White House press secretary Sarah Sanders said in a statement Wednesday has been designated as a national day of mourning, and that the White House flags have already been lowered to half staff to honor Bush.
The Postal Service will suspend regular mail delivery and retail service December 5. The Postal Service will provide limited package delivery service on that day to ensure that the network remains fluid.
The New York Stock Exchange, Nasdaq U.S. equities and options markets and the Chicago Stock Exchange also will be closed on Wednesday.
The Wisconsin Republican was delivering remarks during a ceremony at the Capitol Rotunda where Bush will lie in state, an honor reserved for few.
Dignitaries eulogised the president as a figure who was unfailingly loyal to his country, and members of the military carried his casket from a hearse into the rotunda. His body arrived at Joint Base Andrews.
Bush is shown with his son George W. Bush, who would later become USA president, and wife Barbara Bush in Rye, N.Y., in 1955.
Christy Smith paused over the weekend to pay her respects to President Bush at a bronze statue of him at a Houston park.
Jim McGrath, a spokesman for Bush, tweeted a photo Sunday night of Sully seemingly sleeping by the late president's casket.
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The 41st President, a heroic World War II fighter pilot, left Texas for one final flight to Washington accompanied by his son George W.as well as Laura Bush.
Those reflections will continue throughout the week, when Bush's casket travels from Houston, Bush's hometown, to Washington, DC to lie in state in the United States Capitol. Trump himself has criticized the elder Bush on the campaign trail.
On Thursday, a private funeral service with about 1,200 invited guests will be held at the church starting at 10 a.m. CST.
On Thursday, his casket will rest in a auto pulled by the locomotive during his almost 100-mile final journey from suburban Houston to College Station.
Michelle Obama is canceling two book tour dates to attend President George H.W. Bush's funeral.
Following his presidency, he spent his later years engaged in humanitarian work that would have made a difference in the lives of thousands of persons affected by disasters across the globe.
Use the hashtag#Honoring41 to share your memories/photos of#Bush41. The crew has been tasked by Trump with carrying out "Special Air Mission 41".
Maryland Gov. Larry Hogan is expected to be at the U.S. Capitol to await the arrival of Bush's body, according to the governor's schedule of events.
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's passing on Friday scrambled the congressional calendar and changed the calculation of government shutdown politics.
Ceremonies at the presidential library will include a missing man formation flyover.