They claim that the local authority should now develop a planning policy that better protects island fishermen.
The application from Scottish Sea Farms, which is owned by Salmar AS and the Leroy Seafood Group of Norway, is for a fish farm in Gairsay Sound between the island of Wyre and the north-east of the Orkney mainland.
Fishermen objected because of the impact on the fishing grounds of scallop divers and creel fishermen.
When it was considered on March 26 the vote was tied four each and the deciding vote against was cast by the planning committee's vice chairman, as the chairman had already declared an interest in the matter.
However last month council officials said the decision had been partly based on planning policy from 2004 that specifically related to land-based, not marine, fish farm developments. The council's planning jurisdiction for sea-based fish farms came into effect in 2007.
They took legal advice and the planning committee was recalled on Wednesday when councillors were given a presentation from the applicants on the economic benefits to Orkney of the development. They also heard objections from Fiona Matheson, secretary of the Orkney Fisheries Association (OFA).
After councillors voted six to three to approve the fish farm, she said: "OFA are very disappointed that procedural inexperience has led to a U-turn.
"They have politically aligned themselves with big business against their indigenous fishermen."
She said that OFA would be objecting to the Scottish Environment Protection Agency, over the decision.
The agency awards the licence for such developments.
A spokesman for the local authority said the decision by the Planning Committee was made after careful consideration of arguments put forward by the applicant and objectors, and of planning advice provided by officers.