Previously only those aged over five were eligible.
The new service will help identify people who have been in close contact for at least 15 minutes with someone who has tested positive for Covid-19 and aims to cut off routes of transmission for the virus and control local flare-ups.
"Through testing we hunt down the virus," Mr Hancock said.
"If you have symptoms you must isolate immediately and get yourself a test."
"The virus exists to reproduce and if we can thwart that process we can defeat it," Mr Hancock said.
He added that "we needed to flatten the curve" before introducing contact tracing.
NHS Test and Trace will officially launch across England with the help of 25,000 contact tracers, while an accompanying app is still delayed by several weeks.
Mr Hancock urged the public that it is their "civic duty" to isolate themselves if they are contacted by an NHS contact-tracer from 9am on Thursday.
A close contact is defined as anybody who has been within two metres of an infected person for at least 15 minutes in the two days before symptoms appeared and up to seven days afterwards.
Mr Hancock said the new scheme would help the UK to return to some semblance of normality.
“The big question that we’re all working to answer is this: until an effective treatment or vaccine comes through how can we get back to doing more of the things that make life worth living without risking safety or putting lives at risk?
“NHS Test and Trace is a big part – not the only part – but a big part of the answer to that question.”
He added that by tracking infected people and isolating their contacts, and by continuing social distancing, the national lockdown could be replaced with individual isolation.
“This is national effort and we all have a role”, he added.
“The virus exists only to reproduce – that’s its sole biological purpose, to make as many copies of itself as possible.
“If we can thwart that purpose, we can control the virus and ultimately defeat it.
“We must all follow the NHS test and trace instructions as this is how we control the virus, protect the NHS and save lives.”
Speaking alongside the health secretary was Baroness Dido Harding, the Executive Chair of NHS Test and Trace, who outlined the steps which are involved in the new scheme which she said was essential to easing lockdown further.
If you have one or more of the symptoms of coronavirus - a fever, cough, loss of sense of taste or smell - you must isolate immediately.
You must then book a test on the NHS/coronavirus site or dial 111. If you test positive, you'll be contacted by the NHS test and trace service within 24 hours.
The service will help you establish who you've been in close contact with for at least 15 minutes and who you could have infected.
Anyone you could have infected will then be asked to self-isolate for 14 days, whether they have coronavirus symptoms or not.
Their household members do not need to isolate at this point.
Baroness Harding added: “NHS test and trace is designed to enable the vast majority of us to be able to get on with our lives in a much more normal way, but it requires all of us to do our civic duty.
“We will be trading national lockdown for individual isolation if we have symptoms.
“Instead of 60 million people being in national lockdown, a much smaller number of us will be told we need to stay at home, either for seven days if we are ill or 14 days if we have been in close contact.”
Thanking NHS staff and those who have signed up to be a contact tracer, Baroness Harding said it is one of the "most ambitious and complex programmes ever worked on".
When the health secretary was asked about the delay to the original launch date for the - which was due to launch in mid-May but will not be rolled out for several weeks - he said it was not due to technical problems but added the app is "supposed to complement" the system.
Mr Hancock said the more people cooperate with the test and trace scheme the "greater the room for manoeuvre" for lifting lockdown.
Baroness Harding said the Government could impose restrictions and fines on those who do not comply with the rules, but said ministers were not setting out to be punitive.
She said: "What we’re doing is asking everyone to play their part in protecting themselves, their families, and their loved ones."
"Now, the Secretary of State does have the public health legal ability to impose fines and penalties but that’s not how we’re launching this."
"We will beat this together, rather than making it punitive," she added.
Also speaking at the briefing was England's Deputy Chief Medical Officer, Professor Jonathan Van-Tam explained that without any measures taken, an individual with coronavirus would spread the respiratory disease to three others, meaning it can increase exponentially.
"The extent to which we can keep the virus under control of it very much depends on the extent to which people cooperate with NHS test and trace," Dr Van-Tam said.
Coronavirus: Everything you need to know