As well as a cafe and toilets, the new entrance building will include kiosks, a kitchen and a bike hire point.
The new car park will have electric vehicle charging points and information about the nearby site of a World War Two runway and aerodrome.
At the same time, the National Trust said it wanted to open up eight miles (13km) of new and restored routes, including wildlife trails, cycle tracks, and a wetland habitat area.
It said the new site would be separate from its existing Attingham Park site, and would be free to members, with non-members having to pay a car parking charge to access the site.
A number of people commenting on the plans raised concerns about traffic around the proposed new entrance, but the advice from Shropshire Council planning officers to members of the authority’s planning committee was that the plans should be approved.
A report suggests weight needs to be put on the need to support economic growth.
The National Trust has not said how much the new development would cost.
