"It is with great sadness that we announce the death of our dear father, Captain Sir Tom Moore," his daughters said in a statement.
The 100-year-old, who raised almost £33m for the National Health Service (NHS), was taken to Bedford Hospital after requiring help with his breathing on Sunday.
His daughter Hannah Ingram-Moore said he had been treated for pneumonia over the past few weeks and last week tested positive for Covid-19.
He had not been vaccinated against Covid-19 due to the other medication he was taking.
The Army veteran won the nation's hearts by walking 100 laps of his garden before his 100th birthday.
His endeavour spread joy amid the grim news of the coronavirus outbreak.
He was knighted by the Queen in July.
"The last year of our father's life was nothing short of remarkable. He was rejuvenated and experienced things he'd only ever dreamed of," his daughters said.
"Whilst he'd been in so many hearts for just a short time, he was an incredible father and grandfather, and he will stay alive in our hearts forever."
Raised in Yorkshire, northern England, Moore served in India, Burma and Sumatra during WWII.
"I'm so sorry to hear that Captain Tom has passed away in hospital," British health minister Matt Hancock said on Twitter. "He was a great British hero that showed the best of our country."