The 100-year-old, who raised millions for NHS charities by walking laps of his garden, died with coronavirus in Bedford Hospital yesterday.
The Prime Minister added that the clap would also be for "all those health workers for whom he raised money".
Mr Johnson praised Sir Tom's fundraising efforts and said his was a "life well lived" and that he "inspired the very best in us all".
A minute's silence took place today in the House of Commons before Prime Minister's Questions at noon to honour him and all victims of the pandemic.
Speaker Sir Lindsay Hoyle said Capt Sir Tom "exemplified the best of our values"
Oldhamers have been posting their own tributes to the fundraiser.
