Mito Kaur, 63, was admitted to Glasgow's Queen Elizabeth University Hospital on January 7.
She was one of two patients to test positive for mucoraceous mould and died on March 14.
Her family said they were "devastated" on announcing her death, in a statement via solicitor Aamer Anwar, and said at the time they had "serious concerns" about what happened to her.
Now, NHS Greater Glasgow and Clyde has said an investigation by the prosecution service has found she died from natural causes.
In a statement, the health board said: "The Procurator Fiscal (PF) has concluded that the cause of death was infection with Influenza A&B.
"The PF also stated that mucoraceous mould, while present, did not contribute to the death and as such the PF also concluded that death was from natural causes and was likely unavoidable.
"During the incident management team investigations there was a number of areas inspected for sources of mould with nil found and validation results were satisfactory.
"The hypothesis remains unclear and there were no further infection control investigations required at that time.
"If there had been an ongoing unidentified source we would have expected to see more patient cases."
The heath board said the other patient to test positive for the mould was colonised by the infection as it was present on their skin but was not directly infected by it.
This patient did not require treatment and was discharged.
Last month, Ms Freeman escalated the Government's level of involvement in NHS Greater Glasgow and Clyde, appointing a board to oversee its work, in response to concerns over child deaths following infection at the Queen Elizabeth University Hospital complex.
A public inquiry was earlier announced to examine issues at the hospital site and the delayed Royal Hospital for Sick Children in Edinburgh.