The 100-year-old, who raised almost £33m for NHS charities by walking laps of his garden, was admitted to Bedford Hospital on Sunday.
The Queen led tributes to Capt Sir Tom, “recognising the inspiration he provided for the whole nation and others across the world”.
His daughters said they “shared laughter and tears” with their father in their final few hours together.
Announcing his death, Hannah Ingram-Moore and Lucy Teixeira said the last year of their father’s life had been “nothing short of remarkable”.
He was credited with lifting the nation’s spirits and his saying “Tomorrow will be a good day” trended on social media.
He was knighted by the Queen in July in a special ceremony at Windsor Castle.
“He became not just a national inspiration but a beacon of hope for the world. Our thoughts are with his daughter Hannah and all his family.”
The flag above 10 Downing Street has been flying at half-mast in tribute and Mr Johnson has spoken to Mrs Ingram-Moore to offer his condolences.
A tweet from the White House said: “We join the United Kingdom and the world in [honouring] the memory of Captain Sir Tom Moore, who inspired millions through his life and his actions.”