He was admitted to hospital on January 31, after having difficulty breathing.
"It is with great sadness that we announce the death of our dear father," his daughters Hannah Ingram-Moore and Lucy Teixeira announced on Tuesday.
Captain Tom Moore became famous around the world when he walked 100 laps of his back garden before his 100th birthday on April 30, 2020, to raise money for the UK's National Health Service (NHS) during the first wave of the coronavirus pandemic.
His heroics captured the hearts of people everywhere, and he raised almost £33 million.
The Army veteran was knighted by Queen Elizabeth in July in a special ceremony at Windsor Castle.
"We are so grateful that we were with him during the last hours of his life...We spent hours chatting to him, reminiscing about our childhood and our wonderful mother. We shared laughter and tears together.
"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.
"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."
Capt Sir Tom's daughters said the care he received from the NHS was "extraordinary", saying that staff have been "unfalteringly professional, kind and compassionate and have given us many more years with him than we ever would have imagined."
A Buckingham Palace spokeswoman said: "Her Majesty very much enjoyed meeting Capt Sir Tom and his family at Windsor last year. Her thoughts, and those of the royal family, are with them, recognising the inspiration he provided for the whole nation and others across the world."
The flag above 10 Downing Street has been flying at half-mast in tribute.