Julie Carlson, 49, from Airdrie, North Lanarkshire, said her sibling Deborah Faulds, who said she was a victim of three attacks by the TV star, took her own life in 1994 at the age of 31.
The claims are the latest in a large number of allegations against Savile, with evidence of 214 criminal offences having been recorded in 28 police force areas, including 34 rapes.
An official report into decades of alleged abuse by Savile said five offences are known to have been committed in Scotland, with victims across Strathclyde, Fife, Grampian, Lothian and Borders and in the Northern Constabulary area, where he owned a holiday cottage at Glencoe. Ms Carlson reportedly said her sister had told her family of the attacks, but they had not believed her.
She said: "It haunts me that we didn't believe her. It makes me sick.
"It was not until it all came out about Savile that I finally realised she was telling the truth."
Deborah Faulds took her own life while a patient at Birmingham's Readside Clinic where she had been admitted after being diagnosed with paranoid schizophrenia.
She had previously been a patient at Moss Side Hospital in Liverpool, where Savile is known to have paid regular visits during the 1980s.
Ms Carlson added: "My sister was a patient at Moss Side for many, many years.
"Jimmy Savile visited her three times when she was very ill, and Debs told me and my mum he'd abused her.
"We thought because she was mentally ill she was just making it up. But now I know she was telling the truth.
"I know one thing my sister couldn't do is lie, I just wish I had believed her at the time."