Gus and Barbara Johnston applied for resource consent to demolish the building and construct a house, sleepout and garage on the Matau St site. The hearings panel considered the matter last month and its decision has now been made public.
The cottage is not listed in the council register of heritage buildings and the council decided it did not make "a significant contribution to the heritage values of the precinct".
The council had been told the oldest parts of the house dated back to 1895 and it had been modified several times.
Architect Jackie Gillies, of Queenstown, said demolition might be the only option open for the landowners as the building had not been maintained adequately for some time, so refurbishment was unrealistic.
Eight submissions were received from the public, five opposing consent and three neutral.
Concerns were raised by submitters about the loss of the historic cottage and the visual impact of a new house in the heritage precinct.
The Johnstons had already received an Archeological Authority from the New Zealand Historic Places Trust.
The council approved consent, subject to 13 conditions. The stone walls and stone outbuildings must be retained, along with mature walnut trees on the site.
Other conditions covered the design of the house, landscaping and protecting the stone walls and stone sheds from damage during the construction phase.
