In sombre scenes, Bush's coffin arrived draped in the US flag with the late president having spent the past week lying in state in Washington DC.
George W Bush, who is expected to give a eulogy today, greeted the former presidents before taking his seat alongside the rest of the Bush family.
Trump, who is not set to speak at the service, ordered the federal government closed on Wednesday for a national day of mourning.
The US President came face to face with Barack Obama for the first time since his inauguration and Trump received a frosty reception from his longstanding political opponents.
Trump and the Obamas briefly shook hands, while Hillary – who Trump has demanded is jailed over a historic email breach – refused to glance in his direction.
Despite this, political feuds had already been agreed to be set aside, with George P. Bush revealing his late grandfather would have wanted Americans of all political views to unite.
Speaking to CNN, Bush said: "Whether it's him or his staff, I know, and my grandmother, they all wanted all current occupants to be a part of this process."
"We can put politics aside and focus on the greatness of our country and devotion to causes greater than ourselves.
"There's a time for politics and there's a time for governing. It's important for the country to take this time and reflect on the commonalities that we have rather than the differences."
President Trump, who has been praised for his glowing remarks about the late former president since his passing, will attend the service with his wife Melania.
Trump, who skipped an earlier service at the Capitol, will not be a speaker but he won't be targeted during the funeral after cutting a "deal with the Bush family".
As the current President, Trump also has the final say over important funeral details including providing Air Force One to carry the former president’s remains.
He tweeted earlier today: "Looking forward to being with the Bush family. This is not a funeral, this is a day of celebration for a great man who has led a long and distinguished life. He will be missed!"
"You'll see a lot of joy," said Ron Kaufman, who was George H.W. Bush's White House political director in his unsuccessful re-election campaign in 1992.
"It'll show the way of life that people took for granted in many ways and now kind of long for."
Despite the vast number of people attending, Bush Sr was once worried that his funeral would be a non-event when he was planning it in 2011, his spokesman has revealed.
Jim McGrath tweeted: "Briefed in 2011 about his funeral and lying in state, the 41st President asked with typical humility, "Do you think anyone will come?'''
He added: "Tonight, people are waiting hours to pay their respects."
Following Wednesday's service, Bush Sr's casket will depart the Washington National Cathedral and be taken to Joint Base Andrews.
His remains will then be flown to Ellington Field in Houston before it is brought to St. Martin's Episcopal Church where he will lie in repose until tomorrow.
America's 41st president died shortly after 10pm local time on Friday— just eight months after the death of his beloved wife Barbara.
Bush senior served from 1989 to 1993, and eight years later watched his son George W. became the 43rd president.
The elder Bush saw his popularity swell with the US' success in the Gulf War in 1991 but the Republican was defeated in his bid for a second term by Democrat Bill Clinton.
He had also been a World War II hero, Texas congressman, UN Ambassador, CIA director and Ronald Reagan's vice president.
His remains had lied in state in Washington DC for the past three days for mourning where he wore wear special socks before being buried.
Billy Bush blasted for visiting the remains of George H.W. Bush in trainers
Disgraced NBC anchor Billy Bush turned up to mourn the death of his war veteran uncle and former President George H.W Bush – in a pair of white trainers.
Dressed casually and without a tie, Bush appeared to hold back tears and watched on with other family members as the presidents' coffin was draped in the stars and stripes.
The public watched on as the family stood in silence for a few moments under the Capitol Dome before departing.
Bush hit the headlines during the 2016 presidential campaign when a tape surfaced of an interview with Donald Trump. During the audio, the president could be heard making lewd comments on how he treated women.
Trump said: 'You can do anything… grab them by the p*****.'
Bush can be heard laughing on the tape and also joined Trump in a discussion about the appearance of actress Arianne Zucker, who they were both about to do an interview with.
Then a senior anchor on NBC’s ‘Today Show’, Bush was fired following the incident and has largely remained out of the public eye since.
Bush will be wearing grey socks with a number of small jets flying in formation and jet streams behind them, the family’s spokesman Jim McGrath said.
He tweeted: "The 41st President will be carried to his final rest wearing socks that pay tribute to his lifetime of service, starting as an 18-year-old naval aviator in war."
The former US leader flew more than 50 combat missions during World War II and was awarded the Distinguished Flying Cross.
The remains of the 41st president were flown to Washington DC on 'Special Air Mission 41' and landed at Joint Base Andrews at 3.30pm where a hearse was waiting.
What is the Capitol Rotunda?
The Rotunda is in the United States Capitol, also known as the Capitol Building, directly below the Capitol dome.
The Rotunda was built between 1818 and 1824 in Washington DC.
It is connected by corridors leading south to the House of Representatives and north to the Senate.
It is 96ft in diameter and is 48ft tall, to the top of the original walls.
Including the dome, it is 180ft tall.
It is traditionally used for the lying in state of honoured people.
Underneath the Rotunda is a crypt which was to be the resting place of George Washington but this was eventually abandoned.
Several hundred people gathered in downtown Houston for a memorial to the former president.
City organisers encouraged Houston residents to wear their boldest socks in a nod to Bush's well-known sartorial tradition.
Michael Meaux, who worked in the U.S. State Department for Bush's son, former President George W. Bush, called Bush "the last gentleman president that we've had".
A military band and a guard of honour were also there along with 114 crew members of the USS George HW Bush who stood to attention as the plane landed.
Vice President Mike Pence said: "He was so modest, in fact, he never wrote an autobiography but he left a record of his life in the thousands of letters he wrote."
Speaker Paul Ryan said Bush was "great leader and a good man", adding: "He showed us that how we live is as important as what we achieve."
Senate Majority Leader Mitch McConnell called him a "steady hand, staying the course" for the country.
The plane had taken off from Ellington Field Joint Reserve Base, a Texas Air National Guard base where a 21-gun salute was given and a military band played 'Hail to the Chief'.
George W and wife Laura gave a sombre wave as they climbed the stairs to the plane.
Sully, the late president's service dog was also in attendance and was photographed lying in front of Bush's casket at the funeral home on Monday.
He will be reassigned to a wounded veteran at Walter Reed Naval Medical Center near Washington.
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