They will now be able to end quarantine after seven days instead of 10 by providing negative lateral flow results on day six and day seven.
Health Secretary Sajid Javid said it would minimise disruption caused by the rapid spread of the Omicron variant.
He said the change was based on the latest guidance from health experts.
The change comes amid a spike in cases caused by the new Covid variant, which has created staff shortages for businesses, health services and rail services.
The new guidance applies to everyone, regardless of vaccination status.
It also applies to anyone currently in isolation, so people who tested positive or first showed symptoms on Friday last week could end their isolation in time for Christmas Day if they meet the conditions.
But people should not end their isolation early if they are still experiencing symptoms, officials said.
And anyone ending isolation on day seven is strongly advised to limit contact with vulnerable people, not visit crowded or poorly ventilated spaces, and work from home.
People who are not double-jabbed and come in close contact with a positive case must still isolate for a full 10 days.
The move comes after Prime Minister Boris Johnson confirmed no new restrictions would be imposed in England before Christmas Day.
In a video clip, he said there was not enough evidence on Omicron’s severity and the impact of vaccines to justify extra curbs now, but warned he “can’t rule out” further measures after 25 December.
The Scottish and Welsh governments said they would consider whether to adopt the same rule-change, while Northern Ireland said it would not do so “at this time” but would keep it under review.
The rules mean someone who tests positive on either day six or seven will still be able to end isolation after two negative tests 24 hours apart on the following days.