US acting legend Redford, known for his starring roles in Butch Cassidy and the Sundance Kid and The Sting, died aged 89.
In a statement, his publicist Cindi Berger, stated: "Robert Redford passed away on September 16 at his home at Sundance in the mountains of Utah - the place he loved, surrounded by those he loved. He will be deeply missed. The family requests privacy."
The Oscar-winning star of Out of Africa also founded the Sundance Film Festival in Utah.
He guided Ordinary People to a best director Academy Award in 1980. Redford had quit acting in 2018, following his statement in 2016 that he was "tired of acting."
The actor's most recent post on his Instagram handle witnessed him wishing himself a happy birthday on 18 August.
In a sequence of pictures of him from all along his career, he thanked followers for supporting him "through every step", stating it "meant the world" and referenced his success from his initial hit movies to receiving the Presidential Medal of Freedom.
"Coming from a working-class background in Santa Monica, I experienced setbacks failing out of college, losing my mom at a young age. I worked my way through small TV parts, learned on Broadway, and risked it all directing and creating Sundance. Personal tragedies, such as the loss of my son Scott, taught me resilience. It was grit, passion, and a love for art that brought me here."
He went on: "I'm pleased my films, from The Sting to A River Runs Through It, have moved you, sparked conversations, or comforted you. Sundance has given voice to new filmmakers, and my environmental work has inspired some to care for our planet. Your support makes it all worthwhile, thank you for being part of my life."
Redford's other movies included The Candidate, All the President's Men, Indecent Proposal and The Way We Were.
It was Butch Cassidy, a Western drama about two daredevil bank robbers, that made Redford an overnight star, but he was never comfortable with his image as a handsome heartthrob.
"People have been so busy reacting to how I look, it's a miracle I didn't become a self-conscious blob of protoplasm. It's not simple being Robert Redford," he told New York magazine once.
Part of the New Hollywood cinema movement of the late 1960s, he teamed up again with fellow star Paul Newman - with whom he appeared in Butch Cassidy - for crime caper The Sting in 1973, another classic.
Despite their long-running friendship and on-screen chemistry, the pair never again appeared together.
Redford's most significant contribution to film was possibly Sundance Film Festival, which helped to foster independent film-making in the late 80s and early 90s, to coincide with the period that launched his career.
Redford is survived by his wife Sibylle Szaggars whom he wed in 2009, according to CBS News.
He was previously married to Lola Van Wagenen - the couple had four children together before divorcing in 1995.
One of their sons, Scott, died at two months due to sudden infant death syndrome, CBS reports, and James, died of cancer in 2020.
He is survived by two daughters - Shauna, an artist, and Amy, a director.
