The Cornwall Council vote is a major step forward in the bid to finance the stadium on the outskirts of Truro.
The Cornish Pirates rugby club, Inox Group, Truro and Penwith College and Henry Boot Developments were behind the plans for the multi-use stadium.
In an eight-hour debate, members also approved plans for a new football stadium on a separate site nearby.
The stadium is expected to cost £10m, with £2m promised by Truro and Penwith College and the other £8m from a deal still to be done with a supermarket.
March 2011 Cornwall Council agrees to fund stadium business plan
November 2011 Outline planning permission granted
May 2012 Councillors vote against public funding for stadium
January 2014 Developers say supermarket would fund stadium
March 2015 Council defers planning decision on supermarket
July 2015 Prime Minister David Cameron says he 'wants to see the stadium happen'
Ian Connell, Cornish Pirates chairman, said he was "absolutely delighted" at the "excellent news".
He said: "It will be a tremendous boost for our players, for our supporters and for the public throughout Cornwall."
Rob Saltmarsh, of developers Inox Group, said councillors had realised the "significant community benefit" of the stadium.
Mr Saltmarsh said he hoped the government would "stand by their word" following a pledge by David Cameron ahead of May's general election to support the stadium.
He said: "We can now look to meet with the Department for Culture, Media and Sport and ask them if there is any money available."
Mr Saltmarsh said extra government money could be used to expand the scope of the stadium and possibly increase its size to 10,000 seats.
Plans to build a retail development on the Treyew Road site of Truro City Football Club were also approved.
Money from that project is expected to be used to fund a new ground for the football club at Silver Bow, which was also granted planning consent.
A new supermarket expected to fund a 6,000-seat sports stadium for Cornwall has been given planning consent.