The Hywind project will see five turbines operate in waters around 18- 12 miles (20 to 30km) off the coast of Peterhead, Aberdeenshire.
With a total capacity of 30 MW, the scheme is set to be the largest floating wind project announced in Europe.
The Crown Estate said the agreement follows Stavanger-based Statoil's successful demonstration of the world's first full-scale floating turbine, in operation off the coast of Norway since 2009.
It said the deal will enhance the UK's position as a global leader in offshore wind technology development.
Statoil senior vice president for renewable energy, Siri Espedal Kindem, said: "It represents a new step in the development towards a future floating commercial-scale park.
"We look forward to a progressed dialogue with key stakeholders in Scotland including communities, the local supply chain and the authorities. We will continue to mature the Hywind Scotland Pilot Park towards a final investment decision, by conducting marine surveys and concept studies in order to demonstrate technical and commercial feasibility for future offshore floating wind."
The Crown Estate's head of offshore wind, Huub den Rooijen, said: "Investing in new technologies will be crucial to unlocking offshore wind potential over the long term whilst we continue to focus on the current development pipeline."
Scottish Finance Secretary John Swinney said: "Scotland has a huge offshore wind resource but to maximise this opportunity we need to move into deeper water. The lease agreement awarded to Statoil's Hywind project offers the first step towards harnessing this resource."
WWF Scotland director Lang Banks said the announcement could help firmly establish Scotland at the forefront of global moves to generate clean energy from offshore wind.
He said: "Scotland has an estimated quarter of Europe's total offshore wind resource. However, to be fully able to tap into that potential we need to continue to develop ways to operate offshore, especially in deeper waters, and this project will help to do that.
"Successfully developing floating turbines could enable Scotland to secure even more clean energy from offshore wind and help reduce some of the potential impacts associated with traditional seabed-based turbines.
"Alongside energy-saving measures, offshore wind and other renewables have a critical role to play in helping Scotland reduce climate emissions, create jobs and generate export opportunities.
"With careful planning we can harness offshore wind while safeguarding the nation's tremendous marine environment."