In a statement on social media, they said it was a “relief to finally have a clear diagnosis”.
The 67-year-old was diagnosed with aphasia – which causes difficulties with speech – in spring last year, but this has progressed and he has been given a more specific diagnosis, the family said.
They expressed their “deepest gratitude for the incredible outpouring of love”.
The family went on to say frontotemporal dementia is the most common form of dementia in people under 60.
“Today there are no treatments for the disease, a reality that we hope can change in the years ahead,” the statement said.
Willis became a household name in the 1980s and 90s after starring in blockbuster films such as Die Hard, The Sixth Sense, Armageddon and Pulp Fiction.
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He has also been nominated for five Golden Globes – winning one for Moonlighting – and also three Emmys, where he won two.
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