Kevin Rooney attacked mother-of-five Rosina Sutherland, 74, after ransacking her property in the Longstone area of Edinburgh.
He raped her, repeatedly hit her on the head and body, compressed her throat and restricted her breathing during the fatal ordeal on October 29 last year.
Rooney, 26, fled the scene with almost £400, the keys to the property and the victim's walking stick.
He then went to a nearby pub where he used the cash to buy drinks for himself and strangers in the bar.
The killer later told police: "I've murdered someone. If you gie (give) us a fag I'll show you the body."
Rooney, who was on bail at the time of the offence, has 36 convictions spanning a decade. They include a 2004 conviction for lewd and libidinous practices against two boys under the age of 10.
He pleaded guilty to robbery, rape and murder earlier this week after two days of a trial at the High Court in Aberdeen.
Passing sentence at the High Court in Edinburgh, judge Lady Dorrian jailed Rooney for life, as required by law in murder cases.
She ordered him to spend a minimum of 21 years and four months behind bars.
Police branded Rooney's crime "shocking and depraved", after the sentence was passed.
The killer sat with his head in his hands as the details of his murderous act were revealed in court for the first time.
The court heard that, uninvited, Rooney entered Mrs Sutherland's house where she lived alone at some point after 4pm that day. She did not know him.
He ransacked her house, throwing treasured possessions such as family photographs on the floor. He also pulled the telephone cord apart, depriving her of a chance to contact the outside world.
Rooney then raped her, repeatedly struck her in the face, placed his hand over her mouth and nose, and compressed her throat, preventing her from breathing.
She died and was left partially clothed on the floor.
Rooney took around £380 from the house but left behind tracksuit trousers and top, his mobile phone and a library card in his name.
Advocate depute Alison Di Rollo told the court: "From there, the accused went to the Longstone Inn, a nearby public house, where he used the deceased's money to buy drinks for himself and strangers in the pub.
"He drank for some time at the bar, buying lager, cider and shots, playing pool and chatting to staff and customers.
"Throughout, he walked with a limp, and with the deceased's walking stick, telling one person whom he engaged in conversation that he had been shot in the leg while in the Armed Forces.
"The walking stick was noticeably too short for him. The accused is 6ft 3in tall and the deceased was 5ft 3in."
Unemployed Rooney was detained by police in the early hours of the following day, on an unrelated matter.
It was then that he told them: "I've murdered someone. If you gie (give) us a fag I'll show you the body."
Over the next few hours, he made a variety of comments to police, including: "I asked her for the time and pushed her. She was cold. I didn't mean it."
He also told officers: "I went to an old dear's house. I just wanted somewhere to stay. I killed her. I hit her a few times and suffocated her."
Police took him out to try to find the location but he was unable to direct them to the address.
Meanwhile, an alarm was eventually activated at the victim's house after it recorded no activity in the home.
After failed attempts to contact her, Mrs Sutherland's son-in-law was informed and he went round to the house. There, he found her body and the emergency services were called.
Rooney later told police: "Hopefully I'll die cos I'm not doing 15 years for murder. I'm not going to get bail for murder, am I? It was an accident."
When police were alerted to the discovery of Mrs Sutherland's body, the property in Longstone Park was secured as a crime scene and forensic work began. Rooney's DNA was later found on swabs taken from the pensioner's body.
A post-mortem examination found Mrs Sutherland had blunt-force head injuries, suggesting she was punched repeatedly before death.
When Rooney was detained on suspicion of murder, he told police: "I would never steal off an old woman."
He also laughed when asked about the sex attack, and said: "I've got two personalities, I can't help it."
The prosecutor told the court that the victim, who had various medical ailments, lived a quiet, private life that revolved around her family and her cat. She was extremely close to her two sons and three daughters.
Ms Di Rollo said: "The family of Rosina Sutherland has been devastated by this offence and the circumstances of the loss of their much-loved mother.
"Not knowing exactly how much she suffered and imagining what she went through in her final moments has been almost impossible for them to bear."
Defence QC Gordon Jackson said Rooney had taken a "number of substances", and was wandering about when he tried the victim's door for reasons which were unclear.
The lawyer said: "He said to me all the way through events, when he was anxious during the trial, that he found it was difficult because of, in his words, the hell that the family were going through."
Judge Lady Dorrian told Rooney his crime had many aggravating factors, such as his previous convictions, which included sex offences, and breaching a sexual offences prevention order.
She said: "It's aggravated by the fact that you were on bail at the time. It's aggravated by the fact that it took place in the victim's own home, she being a vulnerable elderly lady living in sheltered accommodation; that you pulled apart the telephone cord; that you violently raped her and that you robbed and ransacked her house."
But for the plea of guilty, which came after some family members had given evidence, Rooney would have been jailed for at least 22 years, the judge said.
Detective Superintendent Alan Crawford, of Lothian and Borders Police, said: "This was a shocking and depraved crime and my thoughts at this time are with Rosina Sutherland's family, who have been put through a harrowing ordeal as a result of Kevin Rooney's actions.
"I would like to pay tribute to them for the courage they have shown, and in particular for the assistance they provided officers investigating Rosina's murder.
"It is my sincere hope that they can draw some comfort from the conviction and sentencing of Kevin Rooney for this horrendous crime."
Mrs Sutherland's relatives made no comment at the end of the hearing.
Defence QC Gordon Jackson said Rooney had taken a "number of substances", and was wandering about when he tried the victim's door for reasons which were unclear.
The lawyer said: "He said to me all the way through events, when he was anxious during the trial, that he found it was difficult because of, in his words, the hell that the family were going through."
Judge Lady Dorrian told Rooney his crime had many aggravating factors, such as his previous convictions, which included sex offences, and breaching a sexual offences prevention order.
She said: "It's aggravated by the fact that you were on bail at the time. It's aggravated by the fact that it took place in the victim's own home, she being a vulnerable elderly lady living in sheltered accommodation; that you pulled apart the telephone cord; that you violently raped her and that you robbed and ransacked her house."
But for the plea of guilty, which came after some family members had given evidence, Rooney would have been jailed for at least 22 years, the judge said.
Detective Superintendent Alan Crawford, of Lothian and Borders Police, said: "This was a shocking and depraved crime and my thoughts at this time are with Rosina Sutherland's family, who have been put through a harrowing ordeal as a result of Kevin Rooney's actions.
"I would like to pay tribute to them for the courage they have shown, and in particular for the assistance they provided officers investigating Rosina's murder.
"It is my sincere hope that they can draw some comfort from the conviction and sentencing of Kevin Rooney for this horrendous crime."
Mrs Sutherland's relatives made no comment at the end of the hearing.
Michelle MacLeod, High Court procurator fiscal for the east of Scotland, said the attack was one of the most distressing that prosecutors have had to deal with.
"Kevin Rooney has pleaded guilty to cowardly, brutal and callous crimes," she said.
"He entered the home of an elderly woman, subjecting her to a violent sexual assault before murdering her and, by the efforts of police and prosecutors, he has now been brought to justice.
"His crimes are among the most appalling and distressing that we have dealt with as prosecutors.
"I am grateful to the police and prosecution team for the positive and just outcome of the case. I would also pay tribute to the victim's family for the dignified way in which they have dealt with these appalling crimes."
PA
