The relaxation of border restrictions came into effect at 4am on Monday.
The government said it hoped the move would "reunite people living in the US and European countries with their family and friends in the UK".
Travellers will be required to take a pre-departure test, and a PCR test on or before the second day after their arrival.
The exemption from quarantine for double-jabbed travellers also applies to European countries Norway, Iceland, Switzerland, Lichtenstein, Monaco, Andorra and Vatican City.
Those vaccinated in the US will also need to provide proof of US residency.
Those returning from France however will still be subject to quarantine rules due to the country's coronavirus situation.
Exemptions will not apply to any country added to the UK's red list of travel destinations.
While the changes would be a major boost to the aviation and tourism sectors - which have been severely restricted during the pandemic - the benefit to potential holidaymakers in England may be negligible due to restrictions in destination countries.
The United States, for example, has already announced that most European travellers, including those from the UK, will remained banned from entering the US due to coronavirus fears.
Britons who are US residents or citizens could benefit from the quarantine relaxations when entering England but they would have to quarantine when returning to America.
What does this mean for English holidaymakers? What are the rules elsewhere?
People hoping to go on foreign holidays this year will still be subject to travel restrictions in the EU and US, despite England's border changes - here we take a look at what the rules are in other popular destinations.
Spain has its own travel restrictions on arrivals from the UK however it is likely they would not stop a fully vaccinated person entering the country.
If Britons can prove they've had their second dose of a coronavirus vaccine longer than 14 days before their arrival in Spain, or that they've tested negative within 48 hours prior to their arrival, then they will be able to enter the country quarantine-free.
The same rules apply for Spain's islands such as Ibiza and Mallorca.
France is on the UK's 'Amber plus' list, which means it will be the only country in Europe from which fully-vaccinated travellers must still self-isolate when they arrive back in England.
Entering France from England is much easier, however, with no travel restrictions at all applying to those who have been twice vaccinated - as long as the second dose was more than seven days ago.
Those who have not been double-jabbed can still enter the country but you must provide proof of a negative PCR or lateral flow test taken less than 24 hours before boarding.
Entry to Greece and its various islands is permitted without quarantine for people who can prove they've either been double-jabbed or have tested negative.
Unvaccinated people must show they've had a negative result from a laboratory PCR test taken within the past 72 hours, or a laboratory lateral flow test taken up to 48 hours before entry.
People can also enter Greece with proof that they've tested positive with Covid-19 in the past 30 to 180 days.
People arriving in Italy from the UK are subject to a five day period of quarantine, whether or not they have been vaccinated.
A coronavirus test must be taken on day five with a negative result in order to leave quarantine.
Britons are not permitted to enter the United States regardless of whether they have been fully-vaccinated or have recently tested negative for coronavirus.
The White House on Monday said it would “maintain existing travel restrictions” due to the increasing spread of the virus and rising case rates across Europe.
There are exemptions for permanent US residents and US citizens however these travellers will be subject to the restrictions of the state they are entering, which is likely to mean a period of quarantine.