President Donald Trump is among the dignitaries who plan to attend.
His coffin had earlier left Texas to a 21-gun salute and was carried to Washington on board Air Force One - temporarily renamed Special Air Mission 41 in homage to the late president.
The funeral will come just five days after the 94-year-old, who was the 41st president of the U.S., passed away.
Along with his son, George H.W. Bush will be eulogized by former Canadian Prime Minister Brian Mulroney, whose time in power overlapped with Bush, former US Sen.
After services in Washington, there will be another funeral in Houston on Thursday, followed by burial at the Bush Presidential Library in College Station, Texas.
Bush is the last president to have served in World War II, and as a fighter pilot, his plane was shot down over the Pacific.
"A great joy to welcome home the newest member of our family, 'Sully, ' a lovely, and beautifully trained, lab from America's VetDogs".
State funerals are traditionally held for current or former presidents and other officials designated by the president. Their presence was to commemorate Bush's signing of the Americans with Disabilities Act, the 1990 law that, among its many provisions, required businesses that prohibit pets to give access to service dogs.
Tiger Woods on Saturday recalled George H.W. Bush as a passionate golfer and a "class act", as many across the sports world mourned the death of the 41st USA president.
"Here lies a great man", said Rep. Paul Ryan, the House speaker, and "a gentle soul".
Trump, who has not always uttered kind words about the Bush family, offered nothing but praise in the hours after the former president's death was announced.
Vice-President Mike Pence said there was a "kindness about the man that was evident to everyone who met him".
The two-year-old Sully has been at Bush's side since June, just weeks after the death of the president's wife Barbara, to whom he was married for 73 years.
See photos from Bush's final journey to D.C., including events at the Capitol and National Cathedral.
The federal government and some financial exchanges will be closed on Wednesday for a day of mourning. Flags on public buildings are flying at half-mast for 30 days out of respect for Bush.
Christy Smith paused over the weekend to pay her respects to the late president at a bronze statue of him at a Houston park.