The 38-year-old man was diagnosed with Crimean-Congo haemorrhagic fever (CCHF) when he returned to Glasgow on Tuesday from Kabul, Afghanistan.
He travelled back to Scotland on a connecting flight from Dubai, Emirates flight EK027, which landed at Glasgow Airport at 12.35pm on Tuesday.
The man was treated in isolation at Gartnavel General Hospital's Brownlee Centre, which specialises in infectious disease.
This morning he was flown to London's Royal Free Hospital in isolation facilities with the support of the Scottish Ambulance Service and the RAF.
NHS Greater Glasgow and Clyde said it has contacted three passengers who were sitting near him on the flight from Dubai. It said it has no evidence that the infection was passed on but the three passengers will be monitored.
The risk to all other passengers on the flight from Dubai is "extremely low".
Dr Syed Ahmed, the health board's consultant in public health who is co-ordinating investigations into the case, said: "The risk of person-to-person transmission of Crimean-Congo viral haemorrhagic fever is extremely low as it can only be transmitted by direct contact with infected blood or body fluids.
"It is not a virus which is transmitted through the air. As such, the risk to those who were in close contact with him is minimal. We have already made contact with all the patient's close contacts and they are being followed up appropriately.
"The decision to transfer the patient to the high-security unit at the Royal Free was taken in line with the national protocol for the management of cases such as this."
Moving the patient is in line with the UK-wide protocol for managing diseases of this severity and rarity, the health board said.
The man was admitted to hospital within three hours of his arrival in Glasgow and all appropriate infection control measures were put in place, the health board said.
CCHF is especially common in east and west Africa. It is fatal in around 30% of human cases. Outbreaks can usually be traced to a person having had contact with blood or body fluids from infected animals or people.
Dr Ahmed said the disease is endemic in parts of eastern and southern Europe, central Asia, Africa, the Middle East and the Indian subcontinent.
It is caused by infection with a tick-borne virus (nairovirus) in the family Bunyaviridae.
The onset is sudden with initial symptoms being headache, high fever, vomiting and back, joint and stomach pain. Other symptoms are red eyes, a flushed face, red throat, jaundice and red spots on the roof of the mouth.
In severe cases, changes in mood and sensory perception are common.
As the illness progresses, large areas of severe bruising, nosebleeds and uncontrolled bleeding at injection sites can be seen, beginning on about the fourth day of illness and lasting for about two weeks.
An NHS24 helpline number has been set up for anyone on flight number EK027 to call if they have concerns. It is 0800 858 531 and is open between 8am and 10pm seven days a week.
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