The Department for Transport said the ban on visitors from Kenya, Bangladesh, the Philippines and Pakistan would enter force at 0300 GMT on April 9.
From 4 am local time next week Friday, worldwide visitors who have departed from or transited through these four additional countries on a 40-country red list in the previous 10 days will be refused entry into England.
Passengers arriving from or transiting through the four countries are barred unless they are British or Irish nationals or United Kingdom residents.
Pakistan has been added to Britain's travel "red list", as Pakistani nationals would not be allowed to enter the country from April 9 onwards.
Travel bans are meant to reduce the risk from new coronavirus variants like the South Africa strain, the Department for Transport (DfT) said.
The other nations of the UK - Scotland, Wales and Northern Ireland - have similar lists to those that apply in England.
Britain has the highest number of COVID-19 deaths in Europe. They are based on advice from the Joint Biosecurity Centre.
The data showed the majority of cases of the South Africa variant detected in England so far were linked to global travel and that very few are thought to have come from Europe, the department added.
Which countries are on the red list?
No direct flight bans from the countries will be put in place but passengers are being advised to check their travel plans before departing for England.
Simon Calder, travel editor at The Independent, said the government has "plenty of evidence that there's a risk from new variants of concern coming in from these countries" and is alarmed about numbers.
The UK has set a potential May 17 date for resuming global travel, which is banned except for a few legally permitted reasons.
Overseas holidays are now banned due to Britain's coronavirus lockdown measures, but British Prime Minister Boris Johnson plans to make an announcement on Easter Monday about lifting restrictions in England.