The infection was detected last month. NHS Greater Glasgow and Clyde (NHSGCC) has launched its own inquiry into the deaths.
The cause of one death is still to be determined. The health board said the cause of death of the other patient – who was elderly – was unrelated.
Control measures were immediately put in place after the two cases of Cryptococcus were identified.
A spokesman for NHSGGC said: “Our thoughts are with the families at this distressing time. Due to patient confidentiality we cannot share further details of the two cases.
“The organism is harmless to the vast majority of people and rarely causes disease in humans.”
The infection is caused by inhaling the fungus Cryptococcus, primarily found in soil and pigeon droppings.
NHSGGC said a likely source was found in a non-public area away from wards and the droppings were removed.
The health board said a small number of child and adult patients who are vulnerable to the infection are receiving medication and this has proved effective.
Teresa Inkster, NHSGGC lead consultant for infection control, said: “Cryptococcus lives in the environment throughout the world. It rarely causes infection in humans. People can become infected with it after breathing in the microscopic fungi, although most people who are exposed to it never get sick from it.
“There have been no further cases since the control measures were put in place.
“In the meantime, we are continuing to monitor the air quality and these results are being analysed.
“It remains our priority to ensure a safe environment for patients and staff.”
As an extra precaution the health board has installed portable Hepa filter units in specific areas, which filter the air continuously.
A Scottish Government spokesman said: “Our primary concern, and that of the health board, remains the safety and well-being of the patients and their families at the hospital.
“There is an ongoing review of two isolated cases of an unusual fungal infection within the Queen Elizabeth University Hospital site, which were detected in December 2018.”
He said no further cases have been reported.
The health board said a specific group of patients was being moved within the hospital due to their clinical diagnosis and ongoing treatment.
Opposition MSPs have called for an inquiry into the case.
Scottish Labour’s shadow health secretary Monica Lennon said: “Patients and the wider public need to be reassured as a matter of urgency that this unit is safe.
Scottish Conservative Glasgow MSP Annie Wells said: “It’s vital this situation is brought under control immediately before it escalates. An urgent investigation is required