Elizabeth Iggulden had been in hospital since being discovered by police officers on 27 September.
The officers forced entry into the flat in Adelphi Place, Portobello, where they found the body of 88-year-old Douglas Iggulden.
An inquiry has been ordered into how police responded to the initial incident.
Supt Alan Porte said:  "Police Scotland can confirm that a woman in her 80s passed away tonight at the Edinburgh Royal Infirmary.
"Our condolences are with her family at this time and we continue to offer support to them as required.
"This death is connection with an incident that occurred within a property on Adelphi Place on Sunday, September 27.  The death is currently being treated as unexplained, however the circumstances are not believed to be suspicious.
"A report will be sent to the procurator fiscal."
The Police Investigations and Review Commissioner is looking at the initial response by Police Scotland to a report of concern about the couple's welfare.
BBC Scotland understands the investigation concerns the timing of the police response.
An 89-year-old woman who was found collapsed at home with her husband's dead body has also died.