The secretary of state for energy, Ed Davey, gave his consent to the proposal following a recommendation 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 one of five projects 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 Burbo Bank extension approved by the government. It will also be located off England's north-west coast.
