Kevin Rooney had 33 previous convictions and was on bail when he attacked Rosina Sutherland in her Edinburgh home in October 2011.
The registered sex offender had been released from prison the year before.
The review said until the murder, efforts to manage Rooney by authorities had been reasonably effective.
A significant case review was commissioned by the Edinburgh Offender Management Committee at Edinburgh City Council.
It concluded that a lack of stable accommodation may have increased the risk that Rooney would re-offend. The report said he had been living at 21 different addresses in the 12 months before the attack.
The review has made 13 recommendations for changes in the way sex offenders are managed on release from prison.
Rooney was given a life sentence and told he must serve a minimum of 21 years and four months in prison after he admitted killing Mrs Sutherland after ransacking her home in Longstone.
The court heard he sexually assaulted the pensioner, who had dementia. After the attack he then went on a drinking spree.
He had previously been jailed for sex offences against two boys and breaking the rules of a sexual offences prevention order.
He was on bail at the time of the attack on Ms Sutherland.
A statement, issued through Police Scotland, from the Edinburgh, Lothian and Borders Oversight Group, said: "The report recognised the extensive multi-agency work that was undertaken in an attempt to manage Kevin Rooney and made 13 recommendations for the agencies involved in the management of Kevin Rooney.
"These recommendations were accepted in full and new practices and processes have been implemented to address them.
"Extensive partnership working exists between agencies involved in managing high-risk sex offenders, and we are all committed to keeping our communities safe and will continue to work hard to protect the public."
A review into the rape and murder of a 74-year-old woman by a known sex offender has concluded the attack could not have been reasonably predicted.