The film premieres in theaters Friday in more than a dozen Southern states.
"It's just a love story to Billy," said Benson, who despite a long career as a television and film director is still best known for his days as teen heartthrob in movies such as "Ode to Billy Joe" and "Ice Castles."
"And it's also a love story to trying to do the right thing, just trying your best to be decent and not hurt others and add to the planet."
At the age of 52, Benson has had three open heart surgeries, and he's not easily separated from his wife and children and their home in New York, where he teaches at New York University.
"I was attracted to this project for, I think, all the right reasons for me, and spiritually, the things I believe in," Benson said. "To me, young Billy is just such a good, decent human being. I wanted to make a movie - this sounds trite - but I wanted to make a movie about goodness."
He believes this film will not only appeal now to "anyone, any faith, any skin color" but also has a decades-long shelf life.
Just as "Amadeus" used Salieri to tell the composer's tale, Graham's story is told through the eyes of Charles Templeton, a former evangelist turned nonbeliever who was Graham's lifelong friend. On his deathbed, Templeton tells how Graham held on to his faith in the face of the horrors such as the Holocaust, while Templeton walked away from God.
The 1949 Los Angeles crusade depicted in the film was scheduled to run for three weeks. It lasted eight, helping turn Graham into the leader of a worldwide crusade-based ministry that for six decades packed stadiums with believers, put him on the pulpit in front of millions, and led him to counsel every U.S. president since Harry Truman.
The movie ends with that crusade, with Hammer's Graham at a lectern, superimposed over black-and-white footage of crowds - footage built specifically for the film by using an amalgam of crowds from various meetings.
"Most people know him as a counselor to presidents and addressing the nation, a man with beautiful, silver hair," said Graham's daughter, Gigi, who endorses the movie and has spoken at churches where the movie is screened. "They don't realize he was a tall, gangly fellow who just accepted a call to preach."
The ailing Graham today rarely leaves his home in rural Montreat, a small town in the Blue Ridge mountains of western North Carolina. His wife, Ruth Bell Graham, died last year following a long illness, and the 89-year-old has a variety of health problems.
But producer Larry Mortorff, who met with Graham after the movie was finished, described the evangelist as "as very alert. His mind is as clear as anything. He's just weak. But he just pierces you with those blue eyes."
The task of playing the Graham during a relatively unknown time in his life fell to Armie Hammer, the 22-year-old great-grandson of industrialist and philanthropist Armand Hammer in his first major acting role.
He practiced by watching interviews with Graham on YouTube, learning that Graham "has so much spunk and personality that I had no idea about."
He studied Graham's body language in sermons, saving his exact movements for the final scene at the crusade. At the beginning, Hammer said he made Graham's motions "wild and flailing because he hasn't formed himself."
Trying to portray Graham during a relatively unknown time in his life "came with both a blessing and curse," said Hammer, whose next role is as the son of Lucifer in "The Reaper" on the CW network. "Everybody knows Billy Graham. If I don't get up there and don't act just like Billy Graham, people are going to know it."
On the other hand, "everybody tends to know Billy Graham the Christian, the figurehead of Christendom," Hammer said. "Most don't know Billy Graham the human. So I did have a little bit of leeway there. That was kind of my security blanket."
Friday's opening follows special screenings held at about 50 churches across the South. Such screenings and endorsements from the pulpit have helped other films, including "Passion of the Christ," succeed financially even though they weren't typical Hollywood fare.
The independent movie was made without the blessing of Billy Graham Evangelistic Association, the Charlotte-based ministry now run by Graham's eldest son, Franklin.
But at some of those early screenings, a few pastors incorrectly said the movie was backed by the association.
Gigi Graham believes that mistake led to the tension between the filmmakers and her brother, who has said the movie "lacks my father's greatest passion: to preach the Gospel of the Lord Jesus Christ to the world and point men, women and children to the saving power."
Benson said he's perplexed about Franklin Graham's concerns, attributing them to "family politics."
"I think all of us are very confused as to why he would have problems with the movie and why anyone who sees the movie would come away saying anything other than, 'What a great man,"' Benson said.
Association spokesman Mark DeMoss said Franklin Graham has seen the movie, and only wants the public to understand it was made independent of the association.
Gigi Graham said her father at first didn't want to see the film, but following the visit with Mortorff at his home, the evangelist asked when he would be able to watch it.
"It was an honor for me to meet with one of my heroes," Mortorff said. "Billy, in all of our research, led an exemplary life. He's an amazing man."