A petition has been lodged with the Court of Session in Edinburgh.
Mr Trump opposes the 11-turbine European Offshore Wind Deployment Centre, claiming that it will spoil the view from his nearby golf course.
The controversial Trump International Golf Links was opened in Balmedie last summer with the support of politicians and businesses but was strongly opposed by some local residents and environmentalists.
In a statement Mr Trump said: "The legal process started yesterday and I plan on proceeding for as long as required, irrespective of cost. It's unfortunate that we have been forced to seek judicial intervention following the recent decision of the Scottish ministers.
"Vattenfall, AREG and Technip were wrong to propose a project that would totally destroy Aberdeen Bay, and Vattenfall's withdrawal clearly indicates their complete lack of confidence in the economic viability of the facility.
"We will not allow the Scottish Government or any other party to undermine what we have created at Trump International Golf Links and look forward to progressing the development further once this battle is behind us."
The petition, lodged by Trump International Golf Links and The Trump Organisation, asks the court to declare that the decision not to hold a public inquiry and the subsequent approval of the centre in Aberdeen Bay in March were unlawful and seeks to have both decisions reversed.
The centre will lie between 2km and 4.5km off the coast and will be able to generate 100MW, providing energy to meet the needs of as many as 49,000 homes, almost half the number in Aberdeen, the Government has said.
It aims to allow developers and supply chain companies to test new technology offshore before commercial deployment.
Last week, as drilling began at the site of the centre off the Aberdeenshire coast, Swedish energy firm Vattenfall said it is paring back its investment in the development. Majority shareholder Vattenfall said it has to ''prioritise its investments'' and will reduce its stake in the project.
A Scottish Government spokesman said: "The Scottish Government is committed to the successful and sustainable development of an offshore wind sector which could lead to a potential generation of over £7 billion to Scotland's economy and support up to 28,000 direct jobs and a further 20,000 indirect jobs by 2020.
"The decision on the European Offshore Wind Deployment Centre application was made following thorough consideration of all material issues connected with the application, taking into account views of consultees, stakeholders and members of the public.
"This development offers a significant and strategic opportunity to drive the harnessing of Scotland's vast offshore renewables resources forward by providing a site for developers to prove new and innovative solutions in a real-time environment."
WWF Scotland director Lang Banks said: "It's kind of sad to think that Trump has nothing better to do than use his billions to try and undermine Scotland's ambition of becoming a cleaner, greener, job-creating nation.
"He may be happy wasting his own money. But, defending his legal action is likely to cost the Scottish taxpayer too.
"In the end, just like the Scottish Parliament's own inquiry, we hope the court sees through his bluff and bluster and agrees that giving the go-ahead to this development was the right decision.
"Studies estimate that Scotland's offshore wind industry could create 28,000 jobs by 2020 and contribute over £7 billion of investment to the economy. It would be a great pity indeed if Donald Trump was in the end responsible for preventing Scotland creating jobs and boosting its economy."