Pre-departure Covid-19 testing will be required for everyone travelling to the UK from 04:00 GMT on Friday morning.
People arriving by plane, train or boat, including UK nationals, will have to take a test up to 72 hours before leaving the country they are in.
All those arriving from places not on the UK travel corridor list must still self-isolate for ten days.
The plans were unveiled last week, though when and how they would be implemented was not confirmed.
There have been issues with testing availability and capacity, so some countries will initially be exempt, the government said.
For instance, the requirement will not apply to travellers from St Lucia, Barbados, Antigua and Barbuda for six days.
Travellers from Falkland Islands, Ascension Islands and St Helena are exempted permanently.
Hauliers are exempt to allow the free flow of freight, as are air, international rail and maritime crew.
The announcement comes after a further 529 deaths within 28 days of a positive test were reported in the UK on Monday. There were also 46,169 cases reported.
More than 32,000 people are currently in hospital with coronavirus, data shows.
Responding to the news, Tim Alderslade, chief executive of Airlines UK, said: “This is a national health emergency and ministers need to act to keep the country safe.
“It is true that much of the sector has been lobbying for pre-departure testing – but this was always predicated on the government removing or reducing the quarantine period at the same time.
“Now we have both quarantine and pre-departure testing.
“That is why this new policy needs to be a time-limited, emergency measure only, in place not a second longer than necessary, and with a proper review mechanism once lockdown comes to an end.
“We cannot afford for this to be baked in over the whole summer.”
He added: “The focus must be on returning travel to normal as quickly as possible and removing the need to quarantine or take a test as the UK population is vaccinated.
“Ideally, as the vaccination roll-out gathers pace and the most at-risk parts of the country are inoculated, we can start to see the economy, and travel, open up, which would enable the sector to have what will be a critical summer season for aviation.”