Webster, 33, has been suffering from a rare form of Malaria since taking in the opening ceremony of the Olympic Games and is currently in a Rio hospital.
The former Sky Sports anchor had cycled to the Brazil capital for charity – covering 90 miles per day, although dehydration from the feat has been named as a possible contributing factor to Webster’s plight.
In a statement made public late on Thursday, Charlie’s mother Joy said: “Charlotte knows she nearly died, she mouthed to me earlier, ‘Look at all the machines keeping me alive’. Charlotte is really strong but as the doctors keep reminding me, everyone heals differently.
“I am just so thankful that she’s able to communicate with us again. It’s been the worst imaginable time – we have been beside ourselves with worry, but the fact Charlotte is now conscious is amazing.
“Knowing Charlotte, the thing she’ll be most annoyed about is that she’s missed the Olympics.
“She will be especially gutted not to have seen Nicola Adams fight today – there’s a TV on the wall, so hopefully she can at least watch the Women’s Boxing final.”
A spokeswoman for the family added: “Charlie’s family and friends have been incredibly touched by the overwhelming support and love shown to Charlie today. Their main focus now is for Charlie to be stable enough to fly back to the UK.”