The Swiss cable manufacturer will design, supply and connect 57 kilometres of AC cables at the Irish Sea project, linking the 32 MHI Vestas V164-8MW turbines and the substation.
The project, located seven kilometres from the UK's north west coast, could be one of the first offshore projects to install MHI Vestas' 8MW turbine.
Approval for Burbo Bank extension has yet to be given by the UK's secretary of state for energy and climate change Ed Davey. UK examining body, the Planning Inspectorate, submitted its recommendations to the government in June. A decision must be made before 26 September.
It is one of five offshore developments in the UK to be awarded a contract for difference deal from the government, which guarantees a set price for the electricity generated.
ABB previously won another UK contract this year. It was chosen to supply cables to the 400MW Dudgeon contract in the North Sea.