The mass sign-up follows health secretary Matt Hancock's request for 250,000 people to donate their time to help the 1.5 million people isolating for 12 weeks in an attempt to slow the spread of Covid-19.
Mr Johnson said the volunteers will be driving medicines from pharmacies to patients, bringing recovered patients home from hospital and making regular phone calls to check on and support people who are staying on their own at home.
The Red Cross has praised the NHS using volunteers and pointed towards other organisations also available to help those affected by the illness.
"This is one of those once-in-a-lifetime moments where a single action from one person can be the difference between life and death for another, and simple acts of kindness are going to make all the difference in keeping some of the most vulnerable people well and out of hospital".
The Government has issued an urgent call for a quarter of a million people to register as a volunteer for the NHS to help tackle the coronavirus crisis.
Over 400,000 people signed up within 24 hours of a British government call for volunteers to help those stuck at home due to the coronavirus outbreak, Prime Minister Boris Johnson said on Wednesday.
People can sign up to the service here.
"Your help has the potential to make a real difference to some of those most affected by this outbreak, from delivering essential prescriptions to calling to check on the wellbeing of those who are self-isolating".
NHS England medical director Stephen Powis reacted: "Overnight 170,000 people have signed up".
Catherine Johnstone CBE, chief executive of RVS, said: "Human compassion comes to the fore at times of great crisis".
Delivered by the Royal Voluntary service, which was founded in 1938 to mobilise volunteers during the Second World War, the NHS Volunteer Response Team will assist the NHS with three key tasks.
"In 2020 we find ourselves once again facing a daunting national challenge".
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".