Kelly Jones, 41, who had been missing from the Glencolmcille area, was found by the Donegal Mountain Rescue, as well as local volunteers and gardaí, in the Old Rectory in the Glen Valley at 12.30pm.
The Old Rectory is about 600m across the river from the Glencolmcille GAA pitch which had been the headquarters for the search operation.
The rectory is now a holiday home whose owners use it a couple of times a year.
Ms Jones had a US mobile phone but did not have an Irish one. Gardaí tried to phone her a number of times but when she was found the phone’s battery was empty and she was without a charger.
Sergeant Anthony Arnold, one of the officers in charge of the search, said Ms Jones had probably been in the rectory since Monday evening because it had been searched by local volunteers on Sunday and earlier on Monday.
Ms Jones was described by gardaí as “weak and disorientated”, and she had a few grazes.
She was airlifted by Coast Guard helicopter to Sligo General Hospital, where her condition was described as not life-threatening.
Her father Ricky, who was told by the US embassy in Dublin that she had been found, is due in Ireland today or tomorrow.
The Texas-born redhead was last seen on Friday afternoon at the Malinmore hostel where she had been staying stayed.
There was a sighting at 5.30pm on Saturday but there was some doubt cast on that identity.
Kelly, who was attended to by a local doctor before being flown to hospital, had difficulty recalling how she came to be in the rectory, where there was furniture, bedding and running water but no food.
Sgt Arnold said: “Her voice was very weak. She doesn’t know how long she was there. We believe it could have been for up to three days, but we are not certain where she was before that.
“She was quite disoriented. The old rectory is about 200m from the Saturday evening sighting.”
Donegal Mountain Rescue team spokesman Brian Murray, who was involved in the search, which covered over 30sq km this week, said: “She was in a state of hypothermia and that could have affected her attempts to remember how she got there.
“She is a very lucky lady that she was found still alive. Obviously the conditions inside the rectory helped. But usually, on mountain and hill searches, by the time you reach day five rescuers start thinking they are looking for a body.”
Ms Jones, who was travelling around Ireland alone on a break from her work in the catering industry in Charleston, South Carolina, was in the Glencolmcille area for 10 days before she was reported missing from the hostel at Malinmore on Sunday.
She was last seen wearing hill-walking gear.
Ms Jones left clothing, her passport and other belongings in the hostel when she vanished.