His body was flown on a "special mission" by Air Force One as the US prepares for three days of mourning.
His remains will lie in state in Washington DC for three days of mourning where he will wear special socks before being buried.
President Trump and first lady Melania arrived at the U.S. Capitol to pay their respects in an unannounced and brief visit.
The billionaire businessman is planning to attend Bush's state funeral Wednesday at Washington National Cathedral.
But he skipped an earlier service at the Capitol, where Bush was eulogized by Vice President Mike Pence and House Speaker Paul Ryan, among others.
Trump is not expected to speak at the service and has a fractured relationship with the Bush family.
But he has praised Bush since his passing as "just a high-quality man who truly loved his family" and a "terrific guy" who will be missed.
The 41st president 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.
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".
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.
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.
Also on the plane were his sons George W, the 43rd president, and Neil as well as their families.
Former Florida governor Jeb Bush joined the family on the tarmac.
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.
Bush's body will lie in state in the Capitol Rotunda until Wednesday, when a state funeral will take place at the National Cathedral.
Trump tweeted: "Looking forward to being with the Bush Family to pay my respects to President George H.W. Bush."
Former presidents Barack Obama, Bill Clinton and his wife Hillary, as well as Jimmy Carter will also attend. Prince Charles is also expected to attend.
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