The building was used for great political receptions in the 19th century and is currently under the stewardship of St Mary's University College.
'Wonderful news'
It was a tourist attraction in Walpole's time and visitors went to see its fireplaces and gilded ceilings which resembled medieval tombs.
Michael Snodin, of the Strawberry Hill Trust, said: "This is wonderful news for the future of Strawberry Hill.
"We will now be able to work towards the restoration of the building and garden, bringing Walpole's 'little gothic castle' back to its former glory and making it a place everyone can visit and enjoy."
The award is stage one of funding and the Strawberry Hill Trust will now be able to submit a more detailed application for a full grant.