Social gatherings of more than six people will be illegal from Monday, but there are some exemptions.
The change in the law comes as the government seeks to curb the rise in coronavirus cases.
Mr Hancock told BBC Breakfast these exemptions apply for schools, work and some “very special” events like weddings and funerals.
“Other than that the rule is really simple,” he said.
We are expected to find out more about the new restrictions at a press conference being held by the prime minister at 4pm.
The implementation of this rule is “absolutely vital to protect life”, the Health Secretary said.
On the new rules on social distancing, he told Sky News: “Abiding by these rules is absolutely vital to protect life.
“We have seen the increase in the number of cases sadly in the last few days.
“We have seen across Europe there is a second wave that many countries have experienced – some of those countries have then got that second wave under control.
“We are determined to take the action that keeps people safe.
“It is incredibly important that everybody follows these new rules and we will be bringing in strict enforcement so that they can be followed.”
When asked if the new rules would mean that Christmas is cancelled, Mr Hancock told LBC radio: “I hope not but we clearly need to act. This is a really simple rule which says you cannot socialise with more than six people.”
He added: “We want to set out very clearly for everybody – so that everybody has the chance to see these rules, read them and then to follow them, and that’s why it will come into force on Monday.
“You have seen that where there is a big spike like Bolton, that’s where we will take action immediately.
“These rules are so important, every single person in the country needs to know what they are so that we can together get a grip of the virus.”
The legal limit on social gatherings will be reduced from 30 people to six.
It will apply to gatherings indoors and outdoors – including private homes, as well as parks, pubs and restaurants.
It comes as Mr Hancock also said that the pause in a Covid-19 vaccine trial was “not necessarily a setback”.
Gatherings of more than six people will be allowed where the household or support bubble is larger than six, or where the gathering is for work or education purposes.
Mr Hancock said the reason work and education were exempt was because “we need to get through this coronavirus with the minimal impact”.
He added: “But it does mean that when it comes to socialising, we are unfortunately having to put in place these rules because our contact tracing system – which is now excellent – shows that the majority of the transmission of this disease is in social circumstances.”
Exemptions will also apply for weddings, funerals and Covid-secure organised team sports, with a full list to be published by the Government before Monday.
Mr Johnson is expected to tell the press conference: “We need to act now to stop the virus spreading.
“So we are simplifying and strengthening the rules on social contact – making them easier to understand and for the police to enforce.
“It is absolutely critical that people now abide by these rules and remember the basics – washing your hands, covering your face, keeping space from others, and getting a test if you have symptoms.”
Meanwhile Mr Hancock rejected claims that the testing system was failing, telling Sky News that testing capacity was at its highest ever level.
But he said that in the last couple of weeks there had been an increase in demand among people not eligible for tests.
“We have had stories of schools sending a whole year group to go and get a test and that is not appropriate, what is appropriate is that if you have symptoms then get a test.”
On the new social restrictions, Downing Street said chief medical officer Professor Chris Whitty, chief scientific adviser Sir Patrick Vallance and the Government had jointly agreed that urgent action was needed after the rise in coronavirus cases.
Some 2,420 lab-confirmed cases of coronavirus were recorded in Britain as of 9am on Tuesday, following the 2,988 reported in the UK on Sunday, which was the largest daily figure since May.