Corey Swite broke into Olive Hill's apartment in 2006, looking for cigarettes after a night of drinking.
When Hill awoke during the break-in he smothered the 85-year-old woman with a pillow and sexually assaulted her.
Swite confessed to the slaying to undercover RCMP officers during a so-called "Mr. Big" operation in which police posed as criminals.
Swite was convicted of first degree murder in 2009, but the conviction was overturned on appeal.
During a second trial this month, Swite pleaded guilty to second-degree murder, said Crown lawyer Rob Bruneau.
"He was 20 years old at the time of the incident. He had no criminal record at all. It was a horrendous attack. But in all of those circumstances, including his aboriginal heritage, I think 13 years is pretty much right on," Bruneau said.
Bruneau also said he expects no more appeals from the defence.
"One of the benefits of a guilty plea is that the only thing that would be subject to appeal now would be the length of the eligibility for parole, and in the circumstances I would be very, very surprised if there was an appeal of that decision."
Swite has been in custody for five years and will be eligible for parole in 2020.