The authority backed the plans, dubbed Aurora by the club, by 32 votes to nine, with club chairman Stewart Milne saying he was ‘very happy’ after the decision.
Plans were approved by council planning officials last week and were rubber-stamped by the council at a meeting on Monday.
The Dons intend to replace their current home of Pittodrie with a 20,000-seater stadium and training complex on the other side of the city at Westhill.
The club has insisted that there are no viable alternatives to Kingsford, and the new stadium could be completed in time for the start of the 2020/21 season.
The proposal divided residents in the Granite City, with just over half backing the plans.
Milne said in a statement published on Aberdeen’s website: “After 17 years, we are one step closer to a new home that will allow us to meet our vision and ambition for Aberdeen Football Club, our city and our region.
“Together, we can deliver a first-class facility that will make us all proud, unlocking the potential of the club, the Trust and the next generation of football stars and making a positive contribution to the local economy.
“We applaud the Councillors for taking this decision in the face of considerable objections. We are fully aware of and sympathetic to those in Westhill and Kingswells who have objected to our plans.
“I want to reassure them once more that we want to engage with them to deliver community facilities they can all enjoy and benefit from.
“I’d like to sincerely thank all those who have supported our plans and the Aurora campaign: our fans, businesses, community groups, sports organisations and individuals.”
Milne added that, all going to plan, construction could get under way from this summer.
Opponents of the plans have voiced concerns about traffic levels on Westhill and have vowed to seek a judicial review.