A Swedish firm has sought permission from Highland Council, Orkney Islands Council and the Scottish Government for the demonstration project.
Melvich Community Council has opposed the proposal because of concerns it would ruin views across to Orkney.
The proposed site is about three miles (6km) out to sea from Dounreay.
The developer, Hexicon AB, has set up Dounreay Trì Limited to develop the project.
The scheme would also involve laying a subsea cable and building a substation.
The plan has still to be considered by the Scottish Government.
Marcus Thor, project director for Dounreay Trì Limited, said: “We are delighted that the council has agreed with this project and hope that Marine Scotland and the Scottish government can take a timely decision on it.
“This demonstration facility which will be built and operated in Scotland opens up the possibility for a significant increase in offshore wind generation and associated supply chain benefits in Scotland.”
WWF Scotland’s director Lang Banks said floating turbines could potentially provide Scotland with “clean power” in the future.
He said: “This proposal still has a few planning process steps to go through. However, successfully developing floating turbines could enable Scotland and other nations to secure even more clean power from offshore wind in the future. Whatever the outcome of these proposals, we will certainly need lots more conventional offshore wind in the future.
“With the right political support for offshore wind and other technologies, Scotland can be kept on course to secure half of all its energy needs from renewable sources by 2030.
“Research shows that generating half of our energy from renewables by 2030 is both necessary and achievable. We look forward to working with the Scottish Government and others to make sure that the policies needed are put in place to deliver on this ambition.”
Lindsay Roberts, senior policy manager at Scottish Renewables, added: “Scotland is home to approximately 25% of Europe’s offshore wind resource and we are now starting to build out projects which will harness this potential.
“We’re also at the forefront of innovation in this exciting sector and projects like this one are part of a new chapter for our renewable energy industry.
“The Scottish Government has shown its ambition to generate the equivalent of half of all energy consumed from renewable sources by 2030 and offshore wind can play a key role in meeting that ambition.”