The secretary of state for energy, Ed Davey, gave his consent to the proposal by the Planning Inspectorate.
Dong Energy is developing the extension, which will sit alongside the existing Walney 1 and 2 projects, which have a combined 367MW capacity.
The extension will see up to 83 turbines installed 19 kilometres from England's north-west coast.
With this approval, Dong will be able to moved towards a final investment decision.
The Walney extension was to be awarded an early contract for difference subsidy by the government in a non-competitive round of funding.
In September, Dong had its 256MW by the government. It will also be located off England's north-west coast.