The 18th century gardens adjoining the house, once home to poet William Wordsworth, were almost completely destroyed in November 2009 when the area was hit by devastating floods.
The renovation project was one of five winners to take a share of a £100,000 donation to the National Trust from Bovril's Great Outdoors Revival scheme, which supports the restoration of important outdoor areas in the UK.
The trust compiled a shortlist of 75 sites in need of repair work and the final decision was put to a public vote. The funds will pay for the replanting of the terraces, trellising for new fruit trees and roses, a new summer house and the rebuilding of the surrounding walls.
Gardener Amanda Thackeray said: "Thanks to everyone who voted for us, we'll now be able to complete the restoration."