This is the first order for the new machine, which is currently the world's biggest commercially available wind turbine.
Developer Dong said that the choice of Vestas is subject to the wind farm being awarded a contract for difference from the government, allowing it to take advantage of new UK subsidies regime.
Under this system, projects must qualify as affordable in order to receive a fixed strike price for the electricity they supply.
Dong is yet to make a final investment decision on the extension, but it said construction could begin in 2016.
The planned purchase of the V164 is something of a departure for Dong, with the company having chosen Siemens as the supplier for the vast majority of its offshore projects.
According to Windpower Intelligence, the last time Dong opted for Vestas turbines for an offshore project was the 90MW Barrow project in the UK, which went online in 2006.
In a statement, Dong said: "With the V164-8.0 MW turbine, Vestas Wind Systems has increased the competition in the multi-MW offshore turbine market."
In December 2012 Dong and Vestas entered into an agreement to cooperate on a number of test activities for the prototype of the V164 at the Danish test centre in Østerild to accelerate the development of the turbine.
The Burbo Bank Extension has a maximum capacity of 258MW and is located 7 kilometres off the English coast besides the existing 90MW Burbo Bank wind farm.