Scottish Power Renewables is behind the scheme to build 10 tidal turbines, which will generate enough electricity to power more than 5,000 homes.
It put forward plans to invest £40m installing the turbines in the waters off Islay, which offer strong tidal flows and shelter from storms.
The required grid capacity to handle the array is also available in the area.
Finance and Sustainable Growth Secretary, John Swinney commented: "With around a quarter of Europe's potential tidal energy resource and a tenth of the wave capacity, Scotland's seas have unrivalled potential to generate green energy, create new, low carbon jobs, and bring billions of pounds of investment to Scotland. This development - the largest tidal array in the world - does just that and will be a milestone in the global development of tidal energy."
Commentators have said there is a sense of excitement in the marine energy industry over the announcement.
Chief executive of Scottish Power Renewables, Keith Anderson, said: "Today's announcement moves the whole marine renewables industry forward in Scotland and the UK. It is a first in terms of Marine Scotland approval for a tidal project in Scotland, and also a world first for an array of tidal power machines. The understanding we develop from Islay will be essential in delivering the larger planned projects in the Pentland Firth."
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Scottish Power Renewables said the Islay project is the world's first tidal array.
But it could soon be dwarfed by the much larger scheme planned for the Pentland Firth, where there are proposals for 1,600 megawatts of production in the coming years, compared to Islay's 10-megawatt array.
The scheme will use Hammerfest Strom tidal turbines, which have been operating as a generating prototype in Norwegian waters for more than six years, and are being tested in Orkney ahead of work starting on the project next year.
Managing director of the European Marine Energy Centre in Orkney, Neil Kermode, explained: "This has been a long time coming. The big challenge for the industry is getting devices out there and literally getting metal wet. This is the first time that a major energy company has voted with its chequebook and pushed ahead with a tidal energy scheme on this scale."
Scottish Power Renewables applied for consent to construct and operate the demonstrator tidal array within the Sound of Islay in July 2010.
Scotland and the UK generally are seen as world leaders in tidal energy research, but the US and Canada are both investing heavily in the field.
Scottish Renewables Offshore policy manager, Johanna Yates, commented: "This represents a major milestone for the marine energy sector in Scotland with the largest project consent granted to date and renewed confirmation of Scotland's place at the forefront of this promising global industry. The Islay project now looks set to be the world's first tidal power array and, once built, will triple the current capacity of marine energy projects in the UK. Not only does this represent a leap forward in clean, green electricity generated for Scottish homes and businesses from this growing sector, but the use of Scottish manufacturing for the 10 turbines will further feed the supply chain of our offshore renewables industry, bringing high value, sustainable jobs."
There is currently 3.4MW of marine energy installed capacity deployed in the UK.
The Scottish government has a target to meet 80% of electricity demand from renewables by 2020.
(JG)
