Charles Gordon, 52, was ordered to serve at least 17 years in prison before being eligible for parole.
He was found guilty of killing Elizabeth Bowe, 50, at her St Andrews flat on 17 September 2016.
Gordon, who had denied murder, claimed he grabbed his sister by the neck after she threatened to claim he raped her.
He was originally accused of raping her, but that charge was withdrawn.
Solicitor advocate Ian Peterson said: “This was not pre-meditated. It appears to have been because of what happened in the flat that day. He phoned the police. He should get some credit for that.”
The High Court in Glasgow heard Gordon strangled his sister and then called the police at 21:24.
He told a 999 operator: “I think I’ve killed my sister. She’s dead and I’m alive.”
Police who arrived at the scene found Gordon calmly smoking a cigarette while his dying sister, who was naked from the waist down, lay just feet away from him with blood coming from her mouth and a blue dressing gown wrapped round her neck.
Torn pieces of a plastic bag, one of which had Ms Bowe’s blood on it, were nearby.
She was taken to Ninewells Hospital in Dundee where she died on 20 September last year.
Pathologist Dr David Sadler told the court that Ms Bowe died from strangulation.
In evidence, Gordon admitted killing his sister, but not murdering her.
He said: “I grabbed hold of her by the throat with my left hand. I kept a hold of her until she hit the floor. She slumped and went down. When she went down I let her go.”
Det Ch Insp Rory Hamilton, of Police Scotland, said: “Our thoughts remain with the family and friends of Elizabeth at this difficult time.
“Charles Gordon carried out an horrific attack and we note the sentence handed down today.”