The latest restriction brought in by the Department for Transport also affects travellers arriving from Eswatini, Zambia, Malawi, Lesotho and Mozambique.
It will apply from 04:00 GMT on Saturday to people who have travelled from or through any of the specified countries in the last 10 days.
It is understood most flights from the affected countries arrive at airports in England, although it is expected the policy will be formally adopted by the other UK nations.The measures will be in place for an initial period of two weeks.
Meanwhile, Botswana, and the islands of Seychelles and Mauritius, are being removed from the UK list of safe travel corridors as there is a high frequency of travel between the islands and South Africa.The new variant of coronavirus circulating in South Africa is already being seen in other countries, including the UK.
The variant, much like the new UK variant first seen in Kent, appears to be more contagious than previous ones.
Anyone arriving into the UK from most destinations must quarantine for 10 days.
But there are a list of countries exempt from the rules, meaning returning travellers do not need to self-isolate, called the travel corridor list.
Under the latest announcement, the travel corridor with Israel will also end amid concerns about rising infection levels in that country.
However, rules in place across the UK currently ban travel abroad unless for specific reasons.