Community board chairman Alasdair Morrison said the vote was passed four to two, with Geraldine Tait and Nancy Higgins opposed.
Project architect Tim Heath was asked to provide more detail about building the library as an extension to Waitati Hall, after resistance to demolition from some community board members.
Opponents wanted the old library retained as a community meeting room.
At April's community board meeting, a petition with 80 signatures was presented, opposing the demolition plan.
Mr Morrison said the main problem with building on the south side of the library was the disruption to the hall.
It would have needed to close during the six months of construction, he said.
The demolition option was also about $100,000 cheaper, but cost was not the main factor, Mr Morrison said.
The architects also costed another option, on an alternative south-side site, at $125,000 more.
The new library has already been approved by the Dunedin City Council.
The community needed to raise about $250,000 for the library, while the council was chipping in $500,000. Mr Morrison said another $50,000 would come from existing funds.
