The Transport Secretary will make a statement in the House of Commons at 11.30am. He is expected to say those returning from amber list countries will not need to enter Covid isolation at home for 10 days upon return.
The announcement will drastically increase the number of tourist destinations available for families looking to get away this summer.
Holiday favourites such as France and mainland Spain are currently largely off-limits for Britons looking to go on holiday.
However, the change in rules will only relate to measures that must be taken on return. Those hoping to travel internationally may still be required to quarantine upon arrival at their destination, depending on the country's own rules.
Today's announcement will come as a huge boost to the beleaguered travel industry, which has been one of the sectors of the economy worst impacted by the pandemic.
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International travel has been banned for large parts the last 16 months.
The changes could come into place as soon as July 19 when England is expected to move onto Stage 4 of Boris Johnson's roadmap out of lockdown.
Ministers are expected to sign off on the changes to the travel measures - including the exact timing - at a meeting of the Cabinet's Covid-O committee this morning ahead of the statement.
The Government announced its intention to scrap quarantine from amber list countries for those who had the vaccine three weeks ago, but said it needed more time to thrash out the details of the policy.
So far 64.6 percent of the adult population has received two Covid jabs while 86.4 percent has had at least a first injection.
It is hoped all adults will have been offered two vaccines by the start of September.
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It is thought children, who currently are not allowed to get a coronavirus vaccine, will also be exempt from the quarantine rules.
Those who have had two jabs will still be expected to isolate in a specialised quarantine hotel for 10 days if returning from a red list country.
Travel bosses have been eagerly awaiting a relaxation in the rules and said the UK has been stricter on international travel than other countries.
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EasyJet boss Johan Lundgren said: "For too long, Brits have been uncertain of when they can enjoy the same travel freedoms afforded by their jab as those in Europe and this is despite the huge success of our vaccination programme which has now successfully fully vaccinated around two thirds of UK adults."
Paul Charles, chief executive of travel consultancy The PC Agency, advised consumers to "lock in deals" before prices go up as "the Government is likely to announce a vaccine dividend for the fully-jabbed from July 19".
Mr Shapps announcement comes after a range of other changes to coronavirus restrictions were announced by ministers earlier this week.
Health Secretary Sajid Javid has declared an end of the need for close contacts to a coronavirus case to isolate if they have received both vaccines from August 16, while Education Secretary Gavin Williamson said the controversial school bubbles system would not return when schools go back in September.
On Monday Prime Minister Boris Johnson also announced plans to scrap most legal coronavirus restrictions from July 19, including the compulsory wearing of masks in enclosed public spaces.
"We will move away from legal restrictions and allow people to make their own informed decisions about how to manage the virus," he said.
"We will continue to monitor the data and retain contingency measures to help manage the virus during higher risk periods, such as the winter.
"But we will place an emphasis on strengthened guidance and do everything possible to avoid re-imposing restrictions with all the costs that they bring."