Video report by ITV News Correspondent Dan Rivers
People across the country took part in the tribute to the veteran at 6pm on Wednesday, following his death at the age of 100.
Sir Tom’s family said they were "incredibly touched" by the gesture and took part outside their home in the village of Marston Moretaine in Bedfordshire.
Nurses and doctors directly involved in the care of Sir Tom at Bedford Hospital also joined the national clap, while the veteran’s first regiment, The Yorkshire Regiment, tweeted a video calling him “a true inspiration”.
Politicians including Health Secretary Matt Hancock, Labour leader Sir Keir Starmer and Scotland’s First Minister Nicola Sturgeon were also among those to take part in the tribute.
Mr Johnson told MPs before Prime Minister's Questions: "Captain Sir Tom Moore, or Captain Tom as we all came to know him, dedicated his life to serving his country and others.
"His was a long life lived well, whether during his time defending our nation as an army officer and last year, bringing the country together through his incredible fundraising drive for the NHS, that gave millions the chance to thank the extraordinary men and women or our NHS, who've protected us in this pandemic."
He added: "As Captain Tom repeatedly reminded us, please remember, tomorrow will be a good day. He inspired the very best in us all and his legacy will continue to do so for generations to come.
"Mr Speaker, we now all have the opportunity to show our appreciation for him and all that he stood for and believed in.
“That is why I encourage everyone to join in a national clap for Captain Tom and all those health workers for whom he raised money at 6pm this evening.”
At the start, the army veteran had hoped to raise a few pounds for the NHS, the public response staggered him. Video report by ITV News Senior Correspondent Paul Davies
It came after the House of Commons observed a minute’s silence in memory of Captain Sir Tom Moore and others who have lost their lives as a result of the Covid-19 pandemic.
Captain Sir Tom's family later tweeted they would be out supporting the clap in his honour.
Mr Johnson said Captain Sir Tom Moore dedicated his life to serving others, and encouraged people to join in a “national clap” in memory of him.
Speaker Sir Lindsay Hoyle said of Sir Tom: “His dignity and determination in raising money to support the NHS charities caught the nation’s mood at the most difficult time.
ITV News Reporter Nitya Rajan speaks to the postmaster at Captain Tom's home village as community grieves loss of national hero
“He exemplified the best of our values.”
The Second World War veteran was admitted to hospital on Sunday with breathing difficulties. Captain Sir Tom's daughter, Hannah Ingram-Moore, said her father had pneumonia for the last few weeks " and last week tested positive for Covid-19".
He died surrounded by his close family, with one more present on FaceTime.
Nurse Nikki Jones' staff have been helped by Captain Tom's fundraising and Made in Chelsea's Georgia Toffolo was inspired to start her own fundraising for the British Legion in the veteran's name: