The 100-year-old, who raised almost £33m for the 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.
The Army veteran won the nation’s hearts by walking 100 laps of his garden before his 100th birthday.
In a statement, Capt Sir Tom’s daughters Mrs Ingram-Moore and Lucy Teixeira said: “It is with great sadness that we announce the death of our dear father, Captain Sir Tom Moore.
Capt Sir Tom’s daughters said the care he received from the NHS was “extraordinary”.
They said staff had been “unfalteringly professional, kind and compassionate and have given us many more years with him than we ever would have imagined”.
The Army veteran, originally from Keighley in West Yorkshire, came to prominence by walking 100 laps of his garden in Marston Moretaine, Bedfordshire, before his 100th birthday during the first national lockdown.
Capt Tom joined the Army at the beginning of World War Two, serving in India and Myanmar, then known as Burma.
