The move is one of a number of measures announced today (Saturday 27 November) in a briefing by the PM as he set out new rules following the discovery of the new Omicron variant in the UK.
He said travellers would have to self-isolate until they provide a negative test.
Transport secretary Grant Shapps later tweeted to confirm: "All fully vaccinated arrivals to the UK are required to self isolate when they arrive, take a PCR test on or before day 2, and continue to self-isolate until they receive a negative result.
"For those who test positive, they must isolate for 10 days. There will be no change for unvaccinated travellers.
"These are targeted measures to provide confidence and protection, and we will review these measures in three weeks to ensure they are working effectively."
It comes after it was announced four more countries - Angola, Malawi, Mozambique and Zambia – would be added to the UK’s red list from 4am Sunday 28 November.
The move followed the placement of South Africa, Botswana, Eswatini, Lesotho, Namibia and Zimbabwe on the red list from midday Friday 26 November.
Meanwhile rules on face coverings are also to be tightened, with the public required to wear them in shops and on public transport.
Johnson also announced that contacts of people who test positive with a suspected case of the Omicron variant in England will be required to self-isolate for 10 days, regardless of their vaccination status.
"We need to slow down the spread of this variant here in the UK, because measures at the border can only ever minimise and delay the arrival of a new variant rather than stop it all together," he said.
The prime minister said there would be a review of all the new rules in three weeks.
Two cases of the new Omicron coronavirus variant were identified in the UK on Saturday.
The cases were understood to be in Nottingham and Chelmsford and were linked, with both people having recently been to southern Africa, according to reports.
The PM stressed the country needed to "buy time" for scientists to better understand the nature of the new variant.
