Plans for the new tourist facility were submitted by the Trust last summer, following years of wrangling over the future of the development.
The original centre burned down during a fire in 2000.
Mr Wilson said the public rightly expected "some clear direction" from a devolved minister on the matter.
He said his department had "weighed up all the options" before selecting the Trust's ambitious plans.
"I have, therefore, weighed up all options including the merits of referring this application to the Planning Appeals Commission (PAC), either on its own or conjoined with a hearing into the previous unsuccessful application from a private developer," said the Minister.
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"Neither of these options would be of any public benefit and would introduce further delay into the provision of the facility and lengthen the already unacceptably long period during which our top tourist attraction has been without a visitors' centre.
"Clearly this would not be in the public interest. Having considered all matters relevant to this case, I have authorised a Notice of Opinion to approve the National Trust application," he added.
The National Trust's preferred architect, Dublin-based Heneghan Peng, unveiled a design with a "strong environmental basis" in June.
Speaking last year, the Trust's Director for Northern Ireland, Hilary McGrady, said: "We have submitted a full robust planning application befitting the Giant's Causeway World Heritage Site and the surrounding landscape."
"We are confident and determined to deliver visitor facilities which will enhance tourism and benefit the local area and indeed everyone in Northern Ireland."
At the time, the Trust speculated the new centre could be open as early as 2011.
(PR/JM)
