The 33-year-old Team GB ambassador has had dialysis treatment reduced and is planning to return to the UK as soon as possible, her management said.
The former Sky and ITV sports presenter, from Sheffield fell seriously ill on August 6 following a 3,000-mile (4,828km) charity cycle ride, having arrived in Rio a few days earlier.
Webster was admitted to hospital, where doctors initially thought she was dehydrated following the gruelling six-week Ride To Rio challenge.
However, her condition deteriorated after she developed a severe complication from a bacterial infection.
In a message to her nearly 80,000 Twitter followers, Webster said: “I’m told I have thousands of messages of love and support to read once I’m better, so thank you very much for those. The last 16 days have been hell – although I don’t remember most of them.
“I am getting stronger each day and look forward to watching all the Olympic highlights; I hear #TeamGB have triumphed.”
A spokesman for Webster said: “Over the weekend, Charlie’s kidneys responded well to treatment and the dialysis has been reduced to around six hours a day.”