Officers from Staffordshire Police had been searching for Jane Morgan, who was last seen in Bentilee on January 20.
But they have now called off the search after a body was found in Buxton this morning.
The force said: “Sadly, the body of a woman, believed to be 49-year-old Jane, was recovered on Leek Road, Buxton, this morning (Friday 21 January).”
The Buxton to Leek Road had been closed for several hours this afternoon with police saying they were dealing with an incident.
It reopened at around 3.05pm.
Detective Constable Bleaze Johnson, of CID North, said: “Jane’s family have been informed and our thoughts and condolences are with them at this very difficult time.”