The farm, off the Norfolk coast, is expected to power more than 400,000 UK homes every year from the end of 2017.
JDR, which employs about 160 workers in the region, says it will make the cabling at Hartlepool and provide accessories such as connectors, cable cleats, and subsea repair joints.
Bosses say the cables will be used to collect and transmit power from turbines, ahead of it being moved to the mainland.
The contract comes days after JDR won a deal to supply more than 70km of cabling, also made at Hartlepool, for the Nordsee One Offshore Wind Farm, off the German coast.
The firm also previously sent more than 200km of cables to the £1.9bn 175-turbine London Array development.
Andrew Norman, JDR chief executive, said: “The UK has led the global market for offshore wind developments.
“We have been involved right from the start and are delighted to have been selected as a partner for Dudgeon.”
Business Minister Matthew Hancock praised JDR, saying it was an example of UK firm’s successes in the offshore industry.
He added: “I’m delighted this contract has been awarded to JDR, which one of the UK’s premier offshore wind suppliers.
“We are working with the offshore wind industry to bolster a thriving manufacturing industry in the UK, ensuring more energy jobs comes to our shores.”
Earlier this year, JDR was successful in a second successive Government Regional Grown Fund bid.
Bosses told The Northern Echo it aimed to invest heavily at its Hartlepool plant after impressing ministers in the flagship job creation scheme.
Helen Kettleborough, JDR’s director of marketing and communications, said: “We created the factory from scratch and it has received a significant amount of investment to reinforce our position in the offshore energy industry.
“The region is a very important part of our work because it possesses great skills in the offshore energy industries.
“The grant reflects the strength and credibility of our plans for future growth and make Hartlepool a centre of excellence.”
Last week, marine engineering firm Tekmar, in Newton Aycliffe, County Durham, revealed it was also sending cable protection systems to the Dudgeon development.