Stanley and Elsie Wallis bought the land 80 years ago after many years of holidaying in Mount Maunganui.
It was later inherited by their daughter Ynys Fraser, who had a "deep love" for the house.
After Ynys died, her four children decided it was the "right time to let the house go".
Ynys' son Iain Fraser, 73, said the family were "delighted" the property was purchased by another family who "intend to continue using the home to create their own family traditions".
He previously said selling the home had been a "really hard decision" but accommodating everyone at the house was proving more difficult as the family grew.
He said Ynys had 14 grandchildren and 26 great-grandchildren, who had enjoyed many holidays at the house.
"We would just love somebody else to get the pleasure out of the property that we have had but in their own way."
There was a provision in her will for a "significant lump" of money from the house sale to be given to various Rotorua charities.
This included the Rotorua Hospice, QE Health Charitable Trust and St Barnabas Church in Ngongotaha.
Principal of Powers Realty, realtor Sandra Power, said the property was bought by a family who would continue to use it as a bach.
"It is really cool actually because the legacy of the property is going to continue with another family."
Power said she knew there was a chance a family would buy the house when marketing it, describing it as a "special property".
"Properties like this only come along once in a while. Although it is very old and hasn't undergone renovations, it is a really special property and you can feel that inside the house.
"Most people expected a developer to buy it, but we always knew [a family buyer] was a strong possibility."
She said she was not surprised that the house sold for more than double the 2018 capital value.
The 2021 capital value, updated by Tauranga City Council after the property was listed, was $7.145m.
There were "a number" of interested buyers but only one was bidding in the auction.
"It is amazing to get a result like that in the auction room because there are not many people that can pay that amount of money in cash. We are well-versed in how to get a result when there is only one cash buyer.
"There were people were waiting in the wings who sadly missed out."
She said it was an "absolute privilege" to market the house, with the team creating a "blockbuster video" over four days as part of the listing.