Development of the facility at Javelin Park is to begin next summer after being delayed for three years due to legal challenges from campaigners.
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The council's Conservative cabinet voted unanimously in favour of the deal, which allows Urbaser Balfour Beatty to start building the plant.
Previously, the council had refused proposals for the scheme.
However, following a public inquiry, plans for the project were approved by the Secretary of State in January.
A further legal challenge by Stroud District Council at the High Court in July failed to get the decision overturned.
(LM/CD)
