People will be able to join "Christmas bubbles" to allow families to reunite over the festive period.
The UK Government and devolved administrations have agreed the approach despite concerns about the spread of coronavirus.
The temporary easing of measures will allow three households to mix in a bubble from December 23 to 27.
Social distancing will be relaxed within the bubbles, giving people the chance to hug friends and family for the first time in months.
A joint statement issued by the four UK governments said: "As 2020 draws to a close, we recognise it has been an incredibly difficult year for us all.
"We have all had to make significant sacrifices in our everyday lives, and many religious and community groups have already had to change or forgo their customary celebrations to slow the spread of coronavirus and save lives.
"This cannot be a 'normal' Christmas. But as we approach the festive period, we have been working closely together to find a way for family and friends to see each other, even if it is for a short time, and recognising that it must be both limited and cautious."
Each Christmas bubble can meet at home, at a place of worship or an outdoor public place, but existing, more restrictive rules on hospitality and meeting in other venues will be maintained throughout the period.
Welsh First Minister Mark Drakeford told the PA news agency: "We have to recognise that Christmas is a very important time for people, and that you have to have a set of rules that people will be prepared to operate within.
"While I have hesitation, because of the state of the virus in Wales and across the United Kingdom, it is better that we have a common set of arrangements that give people a framework that they can manage within and act responsibly within as well."
Scottish First Minister Nicola Sturgeon said: "We know that for some, contact with friends and family is crucial during this time as isolation and loneliness can hit people especially hard over the Christmas period. The 'bubble' approach aims to reduce this impact."
But she warned there would be no further easing of measures for Hogmanay and "even this short relaxation will give the virus a chance to spread".
She added: "Just because you can mix with others indoors over this time, that doesn't mean you have to.
"If you choose to stick with the rules as they are, then you will be continuing the hard work to beat this virus and prevent its spread."
The plan was agreed following a Cobra meeting chaired by Michael Gove bringing together the Westminster Government and the devolved administrations.
Cabinet Office Minister Mr Gove said the deal would "offer hope for families and friends who have made many sacrifices over this difficult year".
"In coming to this agreement, we have listened to scientific and clinical advice on how best to minimise the risk and reach a balanced and workable set of rules that we hope will allow people to spend time together at this important time of year," he said.
Despite the new measures, families and groups of friends will still face difficult decisions and restrictions on their activities.
The restrictions will prevent bubbles from going to the pub for a Christmas drink.
The bubbles will have to be exclusive over the five-day period, meaning people cannot shift from one group to another - although children whose parents are separated will be allowed to move between them.
People aged over 65 in care homes will not be able to join their families for Christmas.
In families where three children live away from home, they would not all be able to return for Christmas.
However, university students returning from halls at the end of term would automatically form part of their family household.
Although social distancing will not be necessary, people will be advised to exercise restraint and judgment if they plan to mix with vulnerable friends or family.
The measures could see families and friends travelling across the UK on a transport network with limited capacity due to social distancing and Christmas engineering works.
UK Transport Secretary Grant Shapps urged people to "look very carefully" at how they will go home for Christmas - and even consider not travelling.
In other developments:
- There were 2,466 deaths involving Covid-19 registered in the week ending November 13 in England and Wales, according to the Office for National Statistics, the first time the figure has exceeded 2,000 since May.
- Government figures showed a further 608 people had died within 28 days of testing positive for Covid-19 as of Tuesday, bringing the UK total to 55,838, although separate data from UK statistics agencies suggest there have now been more than 71,000 deaths involving the disease in the UK.
- And a further 11,299 lab-confirmed cases of coronavirus were reported on Tuesday, the lowest figure since early October.
- Professor Lucy Yardley, a member of the Government's Sage scientific advisory panel, said there should be more focus on the way people mix inside homes - where people may let their guard down and cleaning may be less rigorous than pubs.
- Travellers arriving in England will be able to end their quarantine period with a negative coronavirus test after five days from December 15.
- English councils will be given new powers to close businesses for up to a week if they fail to make their premises Covid-secure.