The British star was best known for his stage roles, earning critical acclaim for his performances in Noel Coward plays and Shakespeare's The Tempest, Much Ado About Nothing, and Henry IV.
He earned a Tony Award nomination for his stint on Broadway as Boss Whalen in Tennessee Williams' Not About Nightingales, and also won the Society of London Theatre's Olivier Award for the same role.
Redgrave - son of veteran actor Michael Redgrave - also enjoyed a lengthy TV and film career, with notable roles in Four Weddings and a Funeral and 1981 movie Excalibur.
He wrote a biography of his famous father, and also penned a play named Bluntly Speaking.
Redgrave is survived by his son, Luke, and daughter, Jemma, from his first marriage to Deirdre Hamilton-Hill, who died in 1997. He also leaves wife Kika Markham and their two sons, Arden and Harvey.
He suffered a heart attack in 2005, and also battled a bout of cancer, but the cause of his death was unavailable as WENN went to press. In a statement, the Redgraves said he died "very peacefully (and) surrounded by his family."
Tragedy struck the Redgrave family last year (09) when Vanessa's daughter, actress Natasha Richardson, died from a head injury after taking a tumble during a skiing lesson in Quebec, Canada.