Mr Johnson said schools across England will close their gates on Friday until further notice, but urged parents not to leave children in the care of grandparents or older relatives who are at higher risk of becoming seriously ill with coronavirus.
He said meals and vouchers would be provided for pupils who currently receive free school lunches, but said "exams will not take place as planned in May and June".
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Education Secretary Gavin Williamson told MPs that schools in England would be closed from Friday until further notice for all pupils, except the children of key workers and the most vulnerable.
The decision was welcomed by teachers' unions who have called for schools to be closed amid staff shortages - with some reported having a third of staff off sick, or self-isolating because of Covid-19.
Mr Williamson told MPs he wanted to provide parents, students and staff with the "certainty they need" as he announced the closures.
"After schools shut their gates on Friday afternoon they will remain closed until further notice," he said.
"This will be for all children except to those of key workers and where children who are most vulnerable."
Mr Williamson continued: "I know the situation has become increasingly challenging.
"I've said before that if the science and the advice changed, such that keeping schools open would no longer be in the best interest of children and teachers, that we would act - we are now at that stage."
Addressing a Downing Street press conference, Prime Minister Boris Johnson said "exams will not take place as planned in May and June" after the school closures were announced.
The Welsh government said on Wednesday that all schools will close for an early Easter break by Friday at the latest, while First Minister Nicola Sturgeon announced schools in Scotland will also close by the end of the week.
Stormont officials said schools are to close across Northern Ireland from Monday - with the potential to remain that way until summer.
Responding to the announcement, Paul Whiteman, general secretary of school leaders' union NAHT, said the country faces a "truly unprecedented and grave situation".
He said: "Today's decision is a vote of confidence in how schools have responded so far. Schools can be confident they are doing a good job.
"Now, they should also be entitled to expect the necessary support from other organisations with civic responsibilities.
"The situation is moving very quickly, and we have more questions than answers at the moment.
"Whilst NAHT and its school leader members stand ready to assist with this response, there are many complicated issues to address immediately as a result of the government's announcement today.
"This will be our focus in the next few days, to assist our members with this enormous task and to work alongside the DfE to make this work on the ground.
"It will not be easy, but the scale of the crisis means that many solutions will have to be tried even though they are less than perfect."