Germany, Italy and the UK announced on Saturday that they had detected cases of the new COVID-19 variant, Omicron.
The UK reported two confirmed cases that Health Secretary Sajid Javid said were "linked and there is a connection with travel to southern Africa."
"We're not going to stop people travelling but will require anyone who enter the UK to take a PCR test by the end of the second day after their arrival and to self-isolate until they have a negative result," Johnson said during a press conference on Saturday afternoon.
Javid had earlier said on Twitter that the two infected people are self-isolating with their households and contact tracing is being carried out.
"As a precaution we are rolling out additional targeted testing in the affected areas - Nottingham and Chelmsford - and sequencing all positive cases," he added.
He also announced that Malawi, Mozambique, Zambia and Angola have been added to the country's travel red list, alongside South Africa, Botswana, Eswatini, Lesotho, Namibia and Zimbabwe which were added earlier this week.
It means travellers from these countries must book a stay in a quarantine hotel.
The "temporary and precautionary" new rules will be reviewed in three weeks.
Germany, Italy, Belgium also report Omicron cases
Two confirmed Omicron infections were also reported by the Bavarian Health Ministry on Saturday.
The two infected people returned from South Africa on November 24 and have been placed in self-isolation. The health authorities of Germany's southeastern lander called on passengers from the same flight to report to their local health authorities as soon as possible and for anyone who visited South Africa within the past two weeks to do a PCR test.
A suspected case of Omicron has also been reported in the western lander of Hesse.
"Several mutations typical of Omicron were found last night in a traveller returning from South Africa. There is therefore a high level of suspicion and the person has been isolated. The complete sequencing is still pending at the current time," Kai Klose, the region's social affairs minister, said on Twitter.
Italy's Higher Institute of Health (ISS) also announced on Saturday evening that a first case of the Omicron variant had been detected in Italy in a person who had recently been in Mozambique.
"The patient and his family members are in good health," it said in a statement.
They come a day after Belgium became the first European Union member state to report a case from a traveller returning from Egypt.
Dutch authorities are meanwhile sequencing samples from 61 passengers from two planes returning from South Africa on Friday and who tested positive for COVID-19.
EU member states on Friday closed their borders to travellers from seven Southern African countries — Botswana, Eswatini, Lesotho, Mozambique, Namibia, South Africa, and Zimbabwe — because of the variant.
The decision came hours before the World Health Organisation (WHO) gave the variant, first known as B.1.1.529, its name and labelled it a "variant of concern".
The United Nations' health agency stressed that "preliminary evidence suggests an increased risk of infection" with experts also worried that the variant's "large number of mutations" make it more immune to current treatment, including vaccines.
Other countries to have imposed travel restrictions with southern African countries include Canada, and the US.