The ex-governor of California arrived in Texas for the ceremony with girlfriend Heather Milligan.
It came 28 years after the actor was appointed to the President's Council on Physical Fitness and Sports by Bush – a post he held for the last three years of his presidency.
In a statement, Scharzenegger said of the former president: "I will always be grateful to him for his friendship, for embracing me and imparting just a fraction of his wisdom during our time together.
"I count myself lucky for many reasons; but for the opportunity to call George Bush a mentor, I can’t help but think I’m the luckiest man in America."
Schwarzenegger played a key role in Bush's reelection campaign – a job that earned him the nickname "Conan the Republican".
Bush would lose that election to Bill Clinton, with Schwarzenegger then going on to become Chairman of the Governor's Council on Physical Fitness and Sports.
A few years later, the Twins star would be governor of the state.
Around 1,200 mourners were expected at St. Martin's Episcopal Church for the service.
Bush Snr's casket arrived at the Houston church last night in a flag-draped coffin arrived as a military band played.
His body was flown by Air Force One to Houston state funeral service at the Washington National Cathedral in Washington, DC.
His son, George W Bush, his wife Laura and other family members watched as the casket was transferred to the hearse.
It was then driven 45 minutes to the church where Bush worshipped for more than 50 years. Today, 1,200 mourners said their final goodbyes.
Earlier, George Jnr wept as he laid a hand on his father's coffin in front of Donald Trump, Barack Obama, and Bill Clinton.
The former presidents sat in the front row as world leaders and American political elite packed the Washington National Cathedral for the state funeral of – the 41st president of the Unites States.
In a eulogy for his father he said: "To us, his was the brightest of a thousand points of light. He knew that failure is part of living a full life – but he taught us to not be defined by failure".
The former president also told how he had sneaked vodka into his father's hospital room.
Trump, who did not speak at the service, ordered the federal government closed on Wednesday for a national day of mourning.
George HW Bush died at the age of 94 just after 10pm on Friday 30 November at his home in Houston, Texas.
Arnold Schwarzenegger's tribute to George Bush
Today, we’ve lost a great hero. George Bush was an inspiration to all Americans and we will miss him dearly. From the day he first put on his U.S. Navy flight suit and took off into the unknown, he always put his country first. He took on many jobs throughout his long career, and all shared one distinct trait: public service. His greatest legacy is that pure American spirit, that commitment to selflessness that drove him until the very end.
He was born in a time that seemed to produce an endless supply of heroes, but make no mistake: George Bush embodied everything that made the Greatest Generation great.
I will always be grateful to him for his friendship, for embracing me and imparting just a fraction of his wisdom during our time together. Some of my fondest memories are of sledding with him at Camp David and inspiring America to join our fitness crusade by hosting the Great American Workout with him on the White House lawn and listening to his speech advice as we flew between campaign rallies. I will never forget the pride I felt the day he appointed me Chairman of the President’s Council on Physical Fitness and Sports. I loved to hear him surprise people with his wild side — explaining the pure joy he felt as he flew and jumped out of planes. I also loved to hear him explain his passion for this country — it was a true love that knew no petty boundaries or party lines. He taught me so much, but most of all, he taught me the power of serving a cause greater than yourself. I count myself lucky for many reasons; but for the opportunity to call George Bush a mentor, I can’t help but think I’m the luckiest man in America.
President Bush has left us for one last flight but his destination isn’t unknown. He’s flying into the arms of the love of his life, Barbara. This evening, each of us should take a minute to look up and offer him a silent thanks.
He died around eight months after his wife, Barbara passed away.
The funeral followed three days of events in Washington honouring the 41st president.
After the Houston funeral, a special train painted to resemble Air Force One was due to carry Bush’s casket, family and close friends about 70 miles to College Station, where he will be buried in a private service alongside his late wife and their daughter Robin, who died of leukaemia in 1953 aged three.
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