International Power will take over the rights to the site at Beinn Mhor on Lewis from the landowner. The facility will be capable of providing electricity to around 100,000 homes by 2016.
It is expected to transform the local economy by finally transmitting wind, wave and tidal power to the mainland when it becomes fully operational.
Angus Campbell, leader of the Western Isles Council, hailed the rights announcement as "excellent news" for the isles.
He added: "This scheme will produce significant employment for the islands in addition to the wider community benefit anticipated and will enable the islands – home to one of the strongest and most consistent wind regimes in Europe – to start contributing meaningfully to Scottish, UK and European carbon reduction targets."
International Power, which was part of National Power and is now 70% owned by the giant French utility company GDF SUEZ, has bought the rights to develop the wind farm, which has already received planning permission for 39 giant turbines.
The London-based firm has agreed to underwrite part of the £400m interconnector to the mainland which is due to be completed by 2015, and have put down a deposit of £20m.
It takes over from landowner Nick Oppenheim, who had originally wanted to build 133 turbines on his Eisgean Estate in the South Lochs area of the island.
This was later reduced to 53, but a public inquiry was held and the inquiry reporter concluded the development would compromise the objectives and integrity of the South Lewis, Harris and North Uist National Scenic Area.
The plans were redrawn to exclude the scenic area and consent for 33 was granted in January 2010. However at the end of that year a six turbine extension was permitted.
Construction is expected to start by 2013 and the wind farm will be fully operational in 2016. As well as precious jobs it should generate millions of pounds in community benefit for wider investment.
Steve Riley, chief executive and president of International Power Europe, said: "This project is a positive step for us in developing a major wind portfolio in Scotland. It will provide a significant boost to the local economy as well as help to secure future UK energy supply from renewable sources."
Mr Campbell said the council, which recommended the scheme for approval, had been working closely with the firm to maximise local opportunities.
He added: "This scheme marks the start of the regeneration of our local economy through renewable energy."
Mr Campbell said the scheme unlocked the proposed interconnector, which would "connect these islands to the main UK Grid by 2015 and will facilitate the investment of over £1 billion in a range of island projects".
He said the council was currently engaged with the UK energy minister and Ofgem, the energy regulator, to ensure the commitment shown by International Power translated into reasonable transmission charges for generators, on and offshore.
Meanwhile, ministers are still considering Lewis Wind Power's application to build a 42-turbine wind farm near Stornoway.
The company is a joint venture between Amec and EDF Energy. It is working in partnership with the Stornoway Trust, the community owned charitable trust, which owns the site that has been chosen. The council has recommended its approval.