The project, which will be the third largest in Scotland, is likely to consist of 103 Siemens 3.6MW turbines. Originally, the developers wanted to install 127 turbines but 24 were refused following flight control concerns.
The Viking Energy Partnership is a 50-50 joint venture between Scottish and Southern Energy (SSE) and Viking Energy Limited (VEL). The latter is 90% owned by the Shetland Charitable Trust (SCT), an organisation set up on behalf of the community to manage compensation payments from Sullom Voe, Europe's biggest oil terminal.
An application to build the project originally went forward in 2009. However, there have been a number of environmental objections to the project and the RSPB Scotland said it was disappointed there were no further reductions to its size.
Scottish energy minister Fergus Ewing, who granted consent for the project said: "The development includes an extensive habitat management plan covering around 12,800 acres, which will restore peatland and offer benefits to a whole range of species and habitats.
"Last week, figures showed Scotland exceeded our ambitious renewable electricity targets for 2011, with more than a third of our electricity demand coming from renewables."
Viking was originally proposed in 2005 with the aim of building a 600MW wind farm.
Shetland is the windiest part of the UK. The wind farm could expect a load factor of up to 50%, meaning it would produce electricity at close to its maximum capacity for around half of the time, making it the most productive wind farm in Europe.