High Court judge Paul McDermott dismissed the appeals brought by three campaigners, who were concerned about the environmental impact of the project, which is to occupy nearly 166,000 square meters in County Galway, west Ireland.
The project, which was first announced more than two-and-a-half years ago, would be the biggest private investment in western Ireland.
Apple had promised to hide the centre in the forest, make good any damage done and use renewable energy to power the centre.
Planning approval was quickly granted but objections were filed on environmental grounds.
The US firm met five key concerns last year, but were held up again by appeals from three local residents, raising doubts that it would ever be approved.
Irish Prime Minister Leo Varadkar held talks with Apple executives last month, who warned the delay could influence future investment decisions.
Ireland believes the project will create around 300 construction jobs and 150 permanent jobs.
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