According to SSE Renewables, the completed plant would produce 600 megawatts of power.
The plans also include provision for a reservoir, an underground waterway system, an underground power station, a 40-metre jetty, administration buildings, access tunnels, and access roads.
The decision will now be referred to Scottish government ministers.
The council’s south planning applications committee said it had no objection to the proposals "subject to conditions being attached to any approval by Scottish ministers".
According to SSE Renewables, the scheme would be the largest hydro project to be built in Scotland and would cost around £800 million.
SSE onshore renewables director Colin Nicol said: "The report presented to the committee recognises that the scheme would be of overall benefit to the Highlands. We believe it would also make a valuable contribution to meeting our future energy needs by allowing surplus energy to be stored and made available at times of high demand.
"We also recognise that there would be short-term disruption during the construction period and we would continue to work actively with the council, public agencies and with local residents to identify the best ways to reduce and manage these short-term impacts."
Meanwhile, Beatrice Offshore Wind Farm (BOWL), a joint venture partnership between SSE Renewables, and Repsol Nuevas Energias UK, has submitted a planning application to the Moray Council for onshore transmission works associated with connecting the wind farm to the electricity grid.
The transmission works would involve laying 20 kilometres of underground cable from a point to the west of Portgordon as well as construction of a new substation located Blackhillock near Keith.
In April 2012, BOWL submitted an application to Scottish Ministers to develop the Beatrice Offshore Wind Farm in the Outer Moray Firth. The proposed wind farm would generate up to 1,000MW of renewable energy, according to SSE.