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.
He has also been nominated for five Golden Globes – winning one for Moonlighting – and also three Emmys, where he won two.
But his family said last year that Willis would give up acting, as his aphasia was affecting his cognitive abilities.
The new statement on Thursday said they hoped media attention would raise awareness of the actor’s condition.
It said: “Bruce always believed in using his voice in the world to help others, and to raise awareness about important issues both publicly and privately.
“We know in our hearts that – if he could today – he would want to respond by bringing global attention and a connectedness with those who are also dealing with this debilitating disease and how it impacts so many individuals and their families.”
The statement was signed by members of Willis’s family including his wife Emma Heming – with whom he has two daughters – and his former wife Demi Moore and their three daughters.
US journalist Maria Shriver, a prominent campaigner for brain disorder patient care and research, tweeted: “My heart goes out to Bruce Willis and his family, & also my gratitude for shining a much needed light on this disease.
“When people step forward it helps all of us. When people get a diagnosis it’s extremely difficult, but also for most a relief to get a diagnosis.”
Aaron Paul, who starred in America’s Breaking Bad TV crime drama, said Willis was “such a damn legend”, adding: “Love you so much my friend!”
US singer and actress Queen Latifah wrote in a post on Instagram: “God bless you my brother we love you!!! all the best. Thank you and your family for all the entertainment!!!”
Actress Selma Blair, who has multiple sclerosis, simply wrote: “Sending love.”
According to the UK NHS website, frontotemporal dementia is an “uncommon” form of the disease that causes the sufferer problems with behaviour and language.
Symptoms also include slow or stiff movements, loss of bladder or bowel control – although this tends to be later on – and muscle weakness.
