The 82.2-metre long monopiles are 7.8-metres in diametre and weigh 1,182 tonnes each. EEW said these were the largest foundation to be made for the offshore wind industry.
Each monopile takes 30 days to complete, but the company produces two monopiles a week, EEW said.
The firm has completed 40 of 67 monopiles, with the remaining foundations to be finished by June.
The monopiles will be used to support 67 Siemens 6MW turbines at the site, located 129 kilometres off the German coast.
Project owners Highland Group Holdings, Siemens Financial Services, and Copenhagen Infrastructure Partners completed financing for the €1.9 billion project in June 2015.
Veja Mate is due online in 2019.
EEW also constructed the XL monopiles for use at Dong Energy's Gode Wind 1 and 2 projects, nearing completion in the German North Sea.
The Gode Wind XL monopiles, also for Siemens' 6MW turbines, are 66.5-metres long, 7.5-metres in diametre and weigh 940 tonnes.