The 30MW Hywind farm, operated by Norwegian oil group Statoil in partnership with Abu Dhabi's renewable energy company Masdar, is located 25 kilometres (16 miles) off the Aberdeenshire coast.
It will power approximately 20,000 households.
Irene Rummelhoff, executive vice president of Statoil's New Energy Solutions, said in a statement that Hywind "will pave the way for new global market opportunities for floating offshore wind energy".
Mohamed Al Ramahi, chief executive of Masdar, said: "Hywind Scotland is showing that floating wind technology can be commercially viable wherever sea depths are too great for conventional fixed offshore wind power.
"This opens up a number of new geographies, and we are already looking at future opportunities with our partners, " he added.
The technical capacity to allow wind farms to float further out to sea opens up the possibility of faster development for the clean technology, which has often been slowed by public opposition to building giant turbines near homes or at picturesque locations.
The Hywind project includes a 1MWh lithium battery known as Batwind to overcome the challenge many clean energy projects have of storing energy produced at times of low demand.
Scottish First Minister Nicola Sturgeon said Hywind would help Scotland meet its "ambitious climate change targets". Many countries plan to rely heavily on to reduce their use of dirty fuels for power generation.
Together with the battery project, the wind farm "puts us at the forefront of this global race and positions Scotland as a world centre for energy innovation," she said.
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