The actor, who is known for his stage, TV and film work, died surrounded by his family after being taken ill in the early hours of Sunday morning.
A statement issued by Corin's wife, Kika Markham, and family said: "Corin Redgrave has died today. He was taken ill at home in the early hours of Sunday morning. He died very peacefully surrounded by his family. We will miss him so very much."
His family said they would "like to thank St George's Hospital (in London) for their care in his last few days".
A member of the famous acting dynasty, Corin was brother to Vanessa and Lynn Redgrave and the son of actor and director Michael Redgrave.
His daughter, from his first marriage to Deirdre Hamilton-Hill, is the actress Jemma Redgrave. Corin also had three sons.
He was uncle to film and TV star Joely Richardson and to Natasha Richardson, who died last year following a ski accident.
His film roles included Hamish in Four Weddings And A Funeral and Cornwall In Excalibur.
TV credits included, most recently, The Turn Of The Screw last year and The Girl In The Cafe in 2005. In recent years he also appeared in episodes of Spooks, Shameless, Foyle's War and Trial And Retribution.
Corin was diagnosed with prostate cancer in 2000.