Dr Kate Stone, 44, was placed in an induced coma on New Year's Eve following an operation at Glasgow's Southern General Hospital to repair damage to her windpipe.
She was injured by the animal near Fort William in the Scottish Highlands in the early hours of Monday December 30.
Doctors decided to take her off sedation on Tuesday following a successful second operation on her windpipe and she has been moved out of intensive care.
A statement released by a colleague at Dr Stone's print firm Novalia said: "Following a successful second operation on Kate's trachea, doctors made the decision to take Kate off sedation late Tuesday afternoon.
"Over the past couple of days, Kate has slowly been regaining consciousness and becoming more active in terms of communicating with doctors and her family.
"She has been taken out of the intensive care unit and moved to high dependency.
"All signs point to a steady recovery and doctors will continue to monitor her progress over the next couple of weeks."
Dr Stone, from Cambridge, was on a short break with friends when the stag ran towards her and gored her while she was standing outside a private residence in Lochailort.
She was taken to Belford Hospital in Fort William before being transferred by air to the Southern General in Glasgow.