Pauline Cafferkey, from South Lanarkshire, is at a speciialist isolation unit at the Royal Free in north London, where she was treated earlier this year.
She was flown from Glasgow in a military aircraft and people who have been in close contact with her are being monitored by the Scottish health authorities as a precaution.
A statement from the Royal Free said: “The Ebola virus can only be transmitted by direct contact with the blood or bodily fluids of an infected person while they are symptomatic, so the risk to the general public remains low and the NHS has well-established and practised infection control procedures in place.”
Dr Ben Neuman, lecturer in virology at the University of Reading, said he thought Ms Cafferkey’s case was only the second where Ebola is reported to have “reactivated”.
Ms Cafferkey was diagnosed with Ebola in December after returning to Glasgow from Sierra Leone and spent almost a month in an isolation unit at the Royal Free at the beginning of the year.
She has been re-admitted after attending Glasgow’s Queen Elizabeth University Hospital because she felt unwell. NHS Greater Glasgow and Clyde said her condition was a “complication of previous infection with the Ebola virus” and the risk to the public was “very low”.
Ms Cafferkey was a winner of a Daily Mirror Pride of Britain award, which recognise courage and achievement against the odds, with nominees voted by members of the public.
Following her diagnosis, she received an experimental anti-viral drug and blood from survivors of the Ebola disease. She was in a critical condition for two weeks and was discharged from the Royal Free in late January.
She said afterwards that she had felt like “giving up” as her condition became critical. The disease has no known cure and is unpredictable.
A February report from Save the Children, the charity Ms Cafferkey worked for in Sierra Leone, said she was probably infected as a result of using a visor to protect her face rather than goggles.
The most recent outbreak of Ebola mainly affected three countries in West Africa: Guinea, Liberia and Sierra Leone. More than 28,000 cases and more than 11,000 deaths have been reported by the World Health Organisation.