The grant will see the Penleaze Wing at Highcliffe Castle, near Christchurch restored and reopened to the public.
The work is one of the final stages to repair the whole of the Grade I listed building.
The house, owned and run by Christchurch Borough Council was mostly destroyed by a fire in the 1950s.
Nerys Watts, from the Heritage Lottery Fund, said: "These exciting plans mean that the last piece in the conservation jigsaw can be put in place at Lord Stuart de Rothesay's fantasy house."
Once the work is completed, it is hoped the original furniture, currently held at the Victoria and Albert Museum, will be loaned back.
The exterior of the building was restored following a Heritage Lottery Fund grant in 1995.
The castle was built in the 1830s by Lord Stuart de Rothesay and was once home to retail magnate Harry Gordon Selfridge, who lived at the castle between 1916 and 1922.
Plans to repair a derelict wing at a cliff-top mansion in Dorset have been boosted by £2,829,700 of Heritage Lottery Funding.