The answer to this question is complicated, as Glacier Bay is not a single entity, but a group of islands and glaciers in the Gulf of Alaska. The islands and glaciers are privately owned, but the main islands are leased from the US Federal Government.
The US National Park Service manages the park, and it is part of the Alaska National Park System.
The islands and glaciers are owned by a variety of entities, but the main owner is Home Depot. The company leases the islands and glaciers from the US Federal Government, and it pays an annual rent to the government.
The lease expires in 2043, but Home Depot has the option to extend it for an additional 10 years.