ABP owns some of the land in the development site. Developer Able UK had submitted a Development Consent Order which includes compulsory purchase of the land which ABP had earmarked for development.
John Fitzgerald, ABP director Humber said, "We are clearly disappointed not to have convinced Able UK that a compromise could deliver the best outcome for the Humber region. Like everyone on the Humber, we are keen to see the offshore wind industry grow and create new opportunities for the region and its young people."
A special parliamentary committee was formed last year, which rejected ABP's opposition.
Last week, ABP also failed to secure a high court review of the government's decision to allow the £450 million park to go ahead. ABP has now withdrawn from further planning challenges.
Able UK said ABP's decision was "very welcome but well over a year later than it need have been".
The 3.2-square-kilometre quay, on the banks of the River Humber, will be available to offshore wind developers for storage, assembly and installation purposes.
Able UK has said the site could deliver as many as 4,000 jobs and is expected have quays available to the offshore sector from 2018.