The 31-year-old was one of four Vietnamese nationals reported missing to the force on July 21 and who may have been in Bismark House Mill, Bower, Street, Oldham, during a fire on May 7.
He maintained regular contact with his wife until the date of the fire, at which time he said he was in a mill, police said.
Teams have been searching the remnants of the mill since demolition workers discovered human remains indicating three victims on July 23.
Detective Superintendent Lewis Hughes, GMP’s victim identification lead, sent his condolences to Uoc’s family.
“On behalf of all involved in Operation Logan, I send condolences to Uoc’s wife and his loved ones,” he said.
“Specially-trained officers are in direct contact with them and to ensure they are fully updated and supported.
“Inquiries are ongoing to establish why Uoc and other, currently unidentified, individuals were in the mill during the fire. Anyone with information which may assist us should contact Greater Manchester Police or Crimestoppers, anonymously.”
On Friday, a spokesman for Greater Manchester Police named three other people believed to have been in the mill at the time of the fire, who were reported missing on July 21.
The force said Cuong Van Chu, 39, arrived in the UK in June 2019 and maintained regular contact with his wife and children until May 7, but his family had not heard from him since.
The force spokesman said Duong Van Nguyen, 29, had been in the UK for about a year and last contacted his family about three months ago, when he said he was living in an “abandoned house” and looking for work.
The fourth missing person was named as 21-year-old Nam Thanh Le, who arrived in the UK in January and last contacted his family on May 4 when he said he was living in a derelict house in “Dam”, believed to be Oldham, and looking for work.