Specialist underwater teams recovered the leg after it was spotted in the River Irwell in Pendleton, Greater Manchester Police have said.
DNA tests have shown the leg to have been that of Marie Scott, who vanished almost exactly a year ago.
She was reported missing from her home in Hale on 18 December 2017.
According to police there are “not believed to be any suspicious circumstances and no one else is believed to be involved in her disappearance”.
Detective Inspector Simon Akker said: “This is an absolutely heart-breaking development in the investigation to find Marie and her family are understandably distraught by the news.
“Having been personally involved in the search to find Marie and met with her family on a number of occasions, I know the devastating impact this will have on them.
“Our efforts now will focus on doing everything we can to ensure we can provide the family with the support and answers they deserve.”