Trevor Shine, 40, underwent emergency surgery to remove a bullet from his head after he was shot twice by the raiders.
Mr Shine, an American, was alone in the house at the time of the attack but managed to telephone for help despite his injuries.
He was shot after being robbed by the men who knocked on the door of his home in Brookwood, near Woking, Surrey, claiming their dog had been killed.
Mr Shine's condition was described as "comfortable". His wife, Melanie, was at his bedside in Frimley Park Hospital.
Detectives were hunting two men seen walking towards Brookwood railway station shortly after the shooting on Wednesday night.
The gunmen were described as being around 30 years old and scruffy looking. One of them was wearing a camouflage army-type jacket.Reuse content