Stanton was born in West Irvine, Kentucky, to Sheridan Harry Stanton, a tobacco farmer and barber, and Ersel (née Moberly), a cook. His parents divorced when Stanton was in high school; both later remarried.

Stanton had two younger brothers and a younger half-brother. His family had a musical background. Stanton attended Lafayette High School and the University of Kentucky in Lexington where he performed at the Guignol Theatre under the direction of theater director Wallace Briggs, and studied journalism and radio arts. "I could have been a writer," he told an interviewer for a 2011 documentary, Harry Dean Stanton: Crossing Mulholland, in which he sings and plays the harmonica. "I had to decide if I wanted to be a singer or an actor. I was always singing. I thought if I could be an actor, I could do all of it." Briggs encouraged him to leave the university and become an actor. He studied at the Pasadena Playhouse in Pasadena, California, where his classmates included his friends Tyler MacDuff and Dana Andrews.

During World War II, Stanton served in the United States Navy, including a stint as a cook aboard the USS LST-970, a Landing Ship, Tank, during the Battle of Okinawa.

Stanton was never married, though he had a short relationship with actress Rebecca De Mornay in 1981–82. "I might have had two or three [kids] out of marriage," he once told the Associated Press. "But that's another story."

Stanton died aged 91 on September 15, 2017, from heart failure, at the Cedars-Sinai Medical Center in Los Angeles, California. A small marker containing his cremated remains was established in a cemetery in Nicholasville, Kentucky.

Stanton was celebrated in "I Want That Man", a 1989 song recorded by Deborah Harry which begins with the line "I want to dance with Harry Dean". In her memoir, Harry writes that Stanton heard the song and arranged to meet her at a club in London.

Stanton is mentioned in the 2013 song "Christmas in L.A." by The Killers. The song's music video begins with a dialogue between the voices of Owen Wilson and Harry Dean Stanton.

Pop Will Eat Itself released a track titled "Harry Dean Stanton" on their album The Looks or the Lifestyle? His lead role in the film Paris, Texas, was memorialized in Hayes Carll's 2019 song "American Dream" with the lyrics, "like Harry Dean Stanton on a drive-in screen, a tumbleweed blowing through Paris, Texas, he fell down into the American dream."

Ian McNabb recorded the song "Harry Dean Stanton" on his album Utopian, released in January 2021. McNabb noted the following about the track: "I didn't know too much about him and didn't really want to because I knew I had to write a song using his name as the title, so I wrote these lyrics for and around him - I imagined what it must be like to be him - while dropping some of my own experiences into the narrative. I was lurking around Dylan's "Blind Willie McTell" and "Lenny Bruce" - I wanted that atmosphere. I've never claimed to be original."