The 61-year-old was airlifted to King Edward VII Memorial Hospital in Stanley following the incident on Monday.
Reports have claimed that Ardiles needed at least 20 stitches to his head after the accident, which is said to have occurred while he and former Spurs teammate Ricky Villa were filming a documentary.
Villa was also involved in the crash, but it is understood that the 61-year-old has left hospital.
According to the Daily Mail, Ardiles released a statement via the Falkland Islands Government, which said: "Thank you to everyone in the Islands who has helped, without exception.
"From the moment of the accident, the attention and care we have received from the police, the RAF helicopter team, the doctors and nurses here has been world class. Thank you to everyone for your concern, I am fine and doing well."
Ardiles remains in hospital.