Prison spokeswoman JoEllen Smith is cited as saying that Ariel Castro was found hanging in his cell at 9:30pm (2:30am UK time) last night.
Prison medical staff performed CPR before he was transported to a hospital, where he was pronounced dead, she said.
Castro was sentenced to life in prison plus 1,000 years after pleading guilty to 937 counts including kidnapping and rape.
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The EC President said he welcomed a "more realistic tone" as he left discussions with Theresa May, but said more work had to be done.
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The England cricketer will miss Wednesday's One-Day International against the West Indies after he was arrested in Bristol on Monday.