The activist and filmmaker died on Friday after being diagnosed with liver cancer, his wife said.
Redford, an 84-year-old retired actor and director known for films including Butch Cassidy And The Sundance Kid and The Way We Were, has asked for privacy.
Cindi Berger, Redford’s publicist, said: “The grief is immeasurable with the loss of a child. Jamie was a loving son, husband and father.”
“His legacy lives on through his children, art, filmmaking and devoted passion to conservation and the environment.
“Robert Redford is mourning with his family during this difficult time and asks for privacy.”
James’ wife of 32 years, Kyle, shared news of his death on Twitter.
Alongside pictures of the couple and their two children, she said: “We’re heartbroken. He lived a beautiful, impactful life & was loved by many.”
Kyle told the Salt Lake Tribune that James, whose documentary films included The Big Picture: Rethinking Dyslexia, discovered the cancer diagnosis in November last year while awaiting a liver transplant.
His liver disease returned two years ago, she added.
Redford has three other children, including the actress Amy Redford.