The club intends 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.
Councillors yesterday debated a motion supporting the recommendation of planners to approve the project and an amendment from Councillor Marie Boulton, who wanted the application to be rejected.
The local authority backed the plans by 32 votes to nine.
Originally unveiled back in May 2016, the Kingsford stadium plan has divided opinion in Aberdeen, with slightly over half of residents in favour of the relocation.
Aberdeen FC said the new facilities are vital to its future and has claimed the stadium and training ground would create more than 400 jobs and bring millions of pounds into the local economy.
Objections have been raised on grounds including potential traffic issues and loss of green belt land.
The planning application was due to go before councillors for determination last October but was put on hold by the club to allow further discussions with the planning service.
The Stewart Milne Group executive chairman said: “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 and 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.
“I’d also like to pay tribute to our team of advisers and experts who have worked professionally, effectively and tirelessly for almost two years on this application.
“The next steps are to await final approval from the Scottish Government, agree the section 75, work through the conditions with the council, and secure the necessary road and building warrant consents. Assuming these move at pace, we should be in a position to begin construction of phase one this summer.”
The plan still has to be approved by the Scottish Government and a series of planning conditions have to be met.
Planning officials had recommended that the proposals were approved provided there are no live concerts, no sporting fixtures before 7pm on a weekday and the training facilities are only open between 9am and 9pm.
Other conditions specified by the officers include a ban on hot food being sold within 150 metres of the ground, the training pitches close to the houses not being used beyond the “early evening” and the expansion of the footpath leading to the Prime Four Business Park.
Senior planner Gavin Evans told councillors that Aberdeenshire Council, which had earlier objected to the plans, could effectively still stop the application, over the issue of controlled parking zones.
Planners noted in their report: “Should members resolve to approve the application, due to the objection from Aberdeenshire Council, formal notification must be given to Scottish ministers, who would then have the opportunity to ‘call-in’ the application for determination.”
The plan’s opponents No Kingsford Stadium plan to pursue a judicial review of the council’s decision.
A spokesman said: “We have worked tirelessly to prevent the approval of this application.
“It is our view that council officials and councillors have failed in their duty to apply the law in this case and we will now progress our petition for judicial review.”
Should the plans go ahead the new stadium could be completed in time for the start of the 2020/21 season.