Mr Bush Jr, himself a former president, described him as “a noble man, the best father”.
All surviving US presidents attended the funeral, sharing a pew in the US National Cathedral in Washington DC.
Mr Bush senior, who served as the 41st US president between 1989 and 1993, died on Friday at the age of 94.
He will be buried in his home state of Texas, alongside his wife Barbara.
In his eulogy, George W Bush said his father had taught him that “public service is noble and necessary”.
“He accepted failure is part of living a full life, but taught us never to be defined by failure. He showed us how setbacks can strengthen,” he added.
His voice breaking with emotion at the end of his eulogy, Mr Bush said: “Through our tears, let us know the blessings of knowing and loving you. A great and noble man, the best father a son or daughter could have.”
The invitation-only funeral at the National Cathedral was attended by President Donald Trump and his predecessors Barack Obama, Bill Clinton and Jimmy Carter.
The Prince of Wales, German Chancellor Angela Merkel and Jordan’s King Abdullah II were among the world figures there to pay their respects.
Former leaders, including John Major, who was UK prime minister for most of Mr Bush’s term, also attended.
Wednesday has been declared a national day of mourning – many government offices and US stock exchanges are closed.
Following the funeral service, Mr Bush’s flag-draped casket was carried from the cathedral by a military honour guard and was later flown to Texas, arriving in Houston at 23:00 GMT.
The casket will lie in public repose at St Martin’s Episcopal Church until Thursday morning.
There will be a second service before the Bush 4141 – a train which was named in honour of the president – takes his body to its final resting place, next to his wife Barbara at the George HW Bush presidential library.
Jim McGrath, who was Mr Bush’s spokesman, said the president had once wondered if anyone would attend his funeral.