"Sam", as she was known by thousands following her story, has been named as Ashley Menatta, 53, of California.
About five months ago she was found in Carlsbad, Southern California, unwell and with no memory of who she was.
Her nephew identified her from a US NBC 7 television show about her, according to NBC 7 and Sam's Facebook page.
He called his mother who then alerted the authorities.
NBC 7 says Ashley Menatta was born in Pennsylvania and had lived in Flagstaff, Arizona. Several years ago, she moved to Southern California where she lived in La Jolla, Vista and Carlsbad.
She reportedly loved travelling and never married. Her sisters, in Colorado and Maryland, are said to have lost track of her in 2013.
Ms Menatta described an "extremely emotional" reunion with her family. "We were all sobbing," she said. "They're so sorry I had to go through what I did during this time without them."
Ms Menatta was found "barely conscious" by emergency services in Carlsbad in February this year.
She told reporters she had been diagnosed with stage three ovarian cancer after the authorities found her, and doctors removed a tumour the size of a volleyball.
Doctors told her she was likely suffering from "retrograde amnesia" - a type of memory-loss brought on during the onset of a disease.
Her slight Australian accent led many people, including US authorities, to suspect she may originally have been from Australia.
She also had strong memories of swimming at a beach in Perth, in Western Australia, and visiting other Australian holiday spots.
Australian consular officials had offered assistance in solving her case.
Her Facebook page, set up with assistance from a former nurse who got involved in the case, said prayers had been answered.
"Well, we have some great news," the post said.
"'Sam' (Ashley is her name) and I want to thank you all who have been sharing, searching, emailing, posting, private messaging, calling, texting, twittering, NBC Channel 7 in San Diego, Australian News, England News, police, Missing Australians, Australian Missing Persons Register, FBI, interpol, and everyone else!!!!
"We could not have done this with out all of your help!"
A woman whose case sparked a social media hunt after she was found on a US street with amnesia has been identified by her family.