Pauline Cafferkey first became ill from the Ebola virus she contracted while volunteering in Sierra Leone on her return in late December, 2014.
Police Scotlandconfirmed that they had provided an escort "as a matter of course" for the ambulance taking Cafferkey to Queen Elizabeth University hospital.
A spokesperson for NHS Greater Glasgow and Clyde said: "Cafferkey was admitted to the Queen Elizabeth University hospital under routine monitoring by the infectious diseases team. She is undergoing further investigations and her condition remains stable."
She was flown to London's Royal Free hospital, which has a specialist isolation unit for Ebola patients.
First Minister Nicola Sturgeon tweeted: "Sending my very best wishes to PaulineCafferkey. She has already suffered way too much - & all for trying to help others. Thoughts with her."
Cafferkey had nearly died, but when she was pronounced out of danger in January 2015, it was thought the virus had been cleared from her system.
But that October, she became critically ill once again and was admitted again to the Royal Free.
She has had long-term problems as a result of the second attack, including muscle weakness in a leg, which has meant she cannot run as she used to do.
Last month, Cafferkeywas cleared of misconduct over her return to the UK with the virus.
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