In the United States, designation of federal land as "Wilderness" can only be done by the Congress. It is the highest degree of legal protection that exists for federal land, and is an "overlay" on top of its status as a national park or other federal property. Here are links to the law which established the Federal Wilderness Preservation System, and guides the management of all federal wilderness areas, and the specific legislation which designated the Gaylord Nelson Wilderness at the Apostle Islands National Lakeshore. Congress late changed the name twice, eventually arriving at the "Gaylord Nelson Wilderness," in keeping with the Nelson family's wishes and to put the name more in line with other wilderness areas around the country.
NPS Wilderness Management Policy
The NPS has three levels of policy documents, which go from the general to the specific. The following links, in increasing order of detail, provide direction on how the Gaylord Nelson Wilderness is to be managed.
Apostle Islands Wilderness Management
The park's 2011 General Management Plan/Wilderness Management Plan established the framework and direction for managing the Gaylord Nelson Wilderness consistent with Wilderness law and policy. Since 2008, the park has had a "Minimum Requirement Process" to assure that any management actions proposed within the wilderness are both necessary and appropriate for the administration of the area as wilderness; and, if so, determines how the action will be carried out in a manner that minimizes impacts to wilderness resources.