The venture, which is being jointly run by two European energy firms, will produce enough electricity to power about 400,000 homes by 2023.
The $2.8 billion project was given the green light in a final environmental review by the US Interior Department on Monday.
Announcing the review, Laura Daniel Davis from the department said: “The demand for offshore wind energy has never been greater.
“The technological advances, falling costs, increased interest and the tremendous economic potential make offshore wind a really promising avenue.”
The project is a key step for Joe Biden’s administration, which has set a goal to double offshore wind capacity by 2030 and net-zero energy emissions in the power sector by 2035.
America’s offshore wind sector lags far behind Europe and largely consists of a five-turbine farm off the coast of Rhode Island.
However, hopes of bringing an offshore wind farm to Massachusetts have stalled for 20 years amid a well-funded and highly organised opposition by wealthy waterfront property owners.
They included the late Ted Kennedy, the former Democratic senator and brother of president John F Kennedy, who died in 2009, and Rachel Lambert Mellon, a prominent heiress and philanthropist, who died in 2014.
The plan was also opposed by Mr Koch, who made his fortune in fossil fuels, and chaired a local residents group which formed in response to the wind energy project.
In a 2013 interview, Mr Koch revealed his strategy to oppose the wind farm was “delay, delay, delay” .