Experts suspect the coins were likely buried for safekeeping in the turmoil of the Norman Conquest.
It is the largest hoard found in the UK from that period.
The South West Heritage Trust was awarded £4,420,527 by The National Lottery Heritage Fund to buy the hoard.
The trust was also given £150,000 from the Art Fund, alongside smaller grants from the Friends of The Museum of Somerset and the Somerset Archaeological and Natural History Society.
Astill added: “By undertaking this work now, we can help safeguard the building and its collections for generations to come.
“We’re using this closure period as an opportunity to improve the visitor experience throughout the museum.
“Alongside the conservation works, we’ll be enhancing our welcome area, shop and café, while refreshing interpretation and interactive displays.”
The Great Hall has already shut, with the rest of the museum following suit at the start of December for up to three months.