250,000 NHS volunteers are needed to help workers in the health sector by delivering medicines, shopping and support "those who are shielded to protect their own health".
"Simple acts of kindness are going to make all the difference in keeping some of the most vulnerable people well and out of hospital".
"As the next step in that effort, today we launch NHS volunteers".
People who volunteer will be asked to help out those who are less able to help themselves through this crisis, and to offer support to both the NHS and local services who would otherwise be overwhelmed during this hard time.
Also on Wednesday, Mr Johnson said it is "vital" to delay the spread of coronavirus and reduce the number of people needing hospital treatment at any one time as the NHS limited numbers of doctors, nurses and specialist equipment.
He told the programme there had been "outbreaks of altruism and people wanting to help", adding that he was "bowled over" by medics returning to the front line and the response from people signing up to help the vulnerable.
Some charities will also be able to refer people to the service.
"Your help has the potential to make a real difference to some of those most affected by this outbreak".
"I am immensely proud of how the whole country is coming together to help one another".
Stephen Powis, NHS England medical director, said: "Overnight 170,000 people have signed up - that's three a minute to help the NHS".
Mr Hancock said: "I know how anxious people are and while this is a great time of turbulence, it is a moment too that the country can come together in that national effort".
"In 2020 we find ourselves once again facing a daunting national challenge".
Dr Mark Wilson, GoodSAM co-founder, said: "GoodSAM has been saving lives through technology for five years by crowdsourcing resuscitation in cardiac arrest".
Secretary of State for digital, culture, media and sport, Oliver Dowden, said: "Our army of dedicated volunteers is already getting ready to play a crucial part in the coronavirus response".