The outline proposals also include the construction of a number of residential blocks to comprise 910 new homes as well as shops and a hotel.
“I’m pleased to see this scheme approved as it will not only provide a new home for the club, but help regenerate a neglected brownfield site," said the Council's cabinet member for housing, planning and regeneration Steve Curran in a statement.
“There were a number of valid objections to the proposals, but on balance, the committee decided there were sufficient checks and safeguards in the plans that these were outweighed by the benefits," he added.
The plans will now be referred to the Mayor of London and the Secretary of State for approval. Subject to grant of planning consent, Brentford FC expects the stadium to be completed by 2016 and the housing element to be completed by 2023.
