Last summer, Reynolds led a high-profile campaign against the government's planning reforms.
Prior to her role at the Home Office, Ghosh held a variety of civil service roles, including permanent secretary to the Department for Environment, Food and Rural Affairs between 2005 and 2010.
National Trust chairman Simon Jenkins said: "Helen is a distinguished and energetic public servant. We are convinced she is ideal to lead the organisations through what is proving a challenging time. We all look forward to working with her."