The underwater cables will feed electricity generated by the 400 megawatt Dudgeon offshore wind farm into the UK national grid.
The order was received from Dudgeon Offshore Wind, a company owned by Statoil and Statkraft.
Turbines of the Dudgeon wind farm will be located in waters 18m to 25m deep on a 55sq.km site 32km off the coast of the seaside town of Cromer in north Norfolk.
Electricity generated by the wind farm will be brought to shore via a seabed cable at Weybourne Hope, some 5km west of the coastal town of Sheringham.
From there an underground cable will be laid to carry the electricity to Necton, where a purpose-built substation will enable transmission into the national grid.
ABB is to design and supply two 132 kilovolt, three-core AC submarine cables.
Each will be 42km long, running from the wind farm's offshore substation to Weybourne Hope, where they will connect to the onshore cables.
The submarine cables will be made at ABB's high voltage cable factory in Karlskrona, Sweden.
Delivery will start in 2016.
ABB power systems division head Claudio Facchin said offshore wind was a growing renewable resource, with Europe accounting for 70% of new offshore wind generation capacity.
"Transporting electricity from offshore wind farms to the shore and then integrating it into the grid for supply to consumers are key elements," he said.
Dudgeon offshore wind farm asset manager Bjorn Bergemo said the cables would be some of the longest offshore cables ordered so far for a UK offshore wind project.