The consent comes nearly two years after Aberdeen Offshore Wind Farm Ltd, which is 75% owned by Vattenfall and 25% owned by Aberdeen Renewable Energy Group, applied in August 2011.
The site will be used to test next generation wind turbines. However, the wind farm is probably best known for provoking the opposition of TV personality and entrepreneur Donald Trump, who has built a golf course and hotel complex within sight of the wind farm.
Trump has previously referred to the project as "environmentally irresponsible" and has led various promotional campaigns and vocal attacks on the Scottish government's promotion of wind energy.
Recently, Trump's spokesman claimed the project would never get off the ground due to recent financial results for Vattenfall. In response Vattenfall said: "Vattenfall must exercise prudence to adjust to the new reality of uncertain and difficult conditions in the European energy sector.
"Vattenfall's future investment is to focus on a sustainable heat and electricity production by transforming the production to low emitting technologies, provide sustainable energy consumption by delivering smart energy solutions and achieve a sustainable economic performance by pursuing excellence in everything we do."
The project received 465 public representations in support and 148 objections, including strenuous opposition from US tycoon Donald Trump, who said it would spoil views from his golf course near the coast.
The EOWDC will allow wind power developers and equipment manufacturers to test technology in an offshore environment before commercial deployment.
This is a crucial factor in reducing development risks and ultimately capital costs. As yet, the UK has no dedicated offshore test sites, although one is being developed off north-east England.
Consent under the Electricity Act is granted subject to conditions that will mitigate a range of impacts, the Scottish government said.
They include radar and noise concerns alongside navigational safety, vessel management and cable laying plans. Permitting for the substation at Blackdog, Aberdeenshire, is a matter for Aberdeenshire Council.
"Offshore renewables represent a huge opportunity for Scotland; an opportunity to build up new industries and to deliver on our ambitious renewable energy and carbon reduction targets," Scotland's energy, enterprise and tourism minister Fergus Ewing said.