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.