For two months staff at Cambridgeshire and Peterborough NHS Trust (CPFT) have been caring for "Robert", who says he cannot remember details of his life.
A trust spokesman confirmed he was Alvydas Kanaporis, 22, from Lithuania.
The doctor treating him said Mr Kanaporis now faced a "journey" to regain his full memory.
People from around the UK got in touch after the trust put out an appeal to identify the man, who they named Robert.
Mr Kanaporis was found in a park in Peterborough in the early hours of 18 May, with no form of identification on him, no mobile phone and no signs of physical injury which might explain his memory loss.
He was believed to be from either eastern Europe or Russia and could understand some Lithuanian and Russian, a spokesman said.
The story was widely publicised in the Lithuanian media on Friday with one man naming him as Alvydas Kanaporis, a former multimedia student, and claiming to be his brother.
All information was shared with Cambridgeshire Police who had confirmed he was not known to them.
A trust spokesman confirmed Mr Kanaporis' family had contacted them, confirming his identity.
However, they did not know how long he had been in the UK.
Dr Manaan Kar Ray, clinical director of acute care at CPFT, said that his patient had "lost completely his entire autobiographical memory".
He said: "These are the building blocks of our existence, so he finds himself in a really distressing place at the moment."
He hoped identifying "Robert" would "help him piece his life back together".
"When we do get a name... or when we get leads, that will be the beginning of a journey for [him]," he said last week.
He described the length of time Mr Kanaporis had lost his memory as being "extremely rare".
The public response to the trust's appeal had been "tremendous" and having a name would "give our work with him a new focus", Dr Kar Ray added.
A "mystery man" found in a Peterborough park with a "severe case of amnesia" has been named five days after health workers appealed for the public's help.