On Wednesday, it was announced that plans to redesign the Schoolhill building was supported by 27 votes to 15.
The project is believed to cost tens of millions of pounds.
It is understood that Depute Council Leader Marie Boulton said the amended plans were not perfect but offered something new.
Historic Scotland will still have to approve the plans.
Some £10m of Lottery funding has already been earmarked for the project, with the total cost of the investment required over the next four financial years is £30m.
Aberdeen City Council's Chief Executive Valerie Watts said: "Today's news means we have reached an important milestone in the redevelopment of Aberdeen Art Gallery.
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"The redevelopment aims to transform Aberdeen Art Gallery and Cowdray Hall into a world class cultural centre, celebrating art and music in the North-east, and to provide a focal point for the creative industries and Aberdeen's Cultural Quarter.
"This redevelopment will see Aberdeen Art Gallery become a modern venue fit for the city's wonderful collection. This ambitious project will breathe new life into an important building so that works which have been unavailable for some time can be displayed in a dynamic and contemporary setting.
"There is huge potential to showcase the arts and culture of the North-east in a way which will not only attract more tourists to the area, but will benefit Aberdonians of all ages as they explore and enjoy their heritage."
Convener of Education Culture and Sport Committee Councillor Jenny Laing added: "Every year Aberdeen Art Gallery attracts tens of thousands of visitors and its redevelopment will inspire and encourage the people who live, work and visit the city to become more involved with an even bigger range of cultural activity and actively pursue their own creativity."
The redevelopment is expected to begin in the first half of 2015 with the Art Gallery due to reopen in 2017.
(JP/IT)
