Among the 47 countries removed were South Africa, Mexico and Cuba, meaning passengers returning to England from these destinations will no longer be required to enter hotel quarantine.
The countries staying red are Colombia, Dominican Republic, Ecuador, Haiti, Panama, Peru and Venezuela, the Department for Transport said.
Announcing the changes, which come into effect at 4am on October 11, Transport Secretary Grant Shapps said: “The measures announced today mark the next step as we continue to open up travel and provide stability for passengers and industry while remaining on track to keep travel open for good.”
Anyone arriving in the UK from a location in the red tier must spend 11 nights in a quarantine hotel.
This costs £2,285 ($3,104) for solo travellers, making such trips unaffordable for many people.
Changes were also made so travellers visiting England have fewer entry requirements.
Mr Shapps announced that the government would recognise vaccines for arrivals from a further 37 countries and territories, including Brazil, Ghana, Hong Kong, India, Pakistan, South Africa and Turkey.
The decision means fully vaccinated people entering England from these locations will be exempt from quarantine, the pre-departure test and the day-eight post-arrival test.
Passengers will be able to send a picture of their lateral flow test as a minimum requirement to verify test result accuracy and keep prices down when day two tests switch to lateral flow later this month, followed by a free PCR test if positive.
Other passengers who are not fully vaccinated with an authorised vaccine returning from a non-red destination must still take a pre-departure test, a day two and day eight test and complete 10 days self-isolation.
No date has been set for when eligible fully vaccinated arrivals will be able to use a lateral flow test for their day-two test, rather than the more expensive PCR version.
The government said its “ambition” is for this to be in place “for people returning from half-term breaks by the end of the month".
A decision on which countries to remove from England's red list was made following a meeting of government ministers on Thursday.
The devolved administrations in Scotland, Wales and Northern Ireland set their own travel rules but have recently mirrored announcements made in Westminster.
The Department for Transport said: “The continued progress on vaccination both at home and around the world means government can confidently reduce the size of the red list to focus on countries which pose the highest risk.”
Mr Shapps added: “With half-term and winter sun around the corner, we’re making it easier for families and loved ones to reunite, by significantly cutting the number of destinations on the red list, thanks in part to the increased vaccination efforts around the globe.
“Restoring people’s confidence in travel is key to rebuilding our economy and levelling up this country. With less restrictions and more people travelling, we can all continue to move safely forward together along our pathway to recovery.”
Also on Thursday, Abu Dhabi extended its green list of countries and destinations from which travellers can enter the emirate without needing to quarantine on arrival, regardless of their vaccination status.
In the most extensive changes since the green list started, 27 new destinations have been added in Thursday’s update, which will take effect on Friday at 12.01am.
The US and UK have been added to the green list, along with popular European holiday hotspots France and Spain. Romania is the only country to be removed from the list.
Responding to the latest UK government travel announcement, Sean Doyle, chairman and chief executive of British Airways, said: “It finally feels like we are seeing light at the end of a very long tunnel.
“Britain will benefit from this significant reduction in red list countries, and now it's time to turn our attention to eradicating testing for fully vaccinated travellers to ensure we don't lose our place on the global stage.
“Once we have a firm date for the reopening of US borders in November, we look forward to reconnecting our two countries, reigniting transatlantic businesses and reuniting families who have been separated for the best part of two years. We are ready, and we look forward to operating our first flights and welcoming back our customers.”
A Heathrow spokesperson said: “Now that we've got the protections of the vaccine, ministers need to prioritise the safe return of frictionless travel as soon as possible.
“Further progress has been made today by reducing the red list and extending vaccinated status recognition to more countries. Both moves will restore vital trade routes that will kick start a Global Britain.
“However, the missing piece to this is clarity on when cheaper lateral flow tests will be accepted, which is now critical in order to save the half-term getaway for many.”
Airlines UK, the industry body representing UK-registered carriers, said: “We welcome the significant reduction of the red list as another positive step towards normalising air travel and reopening our sector.
“This builds on recent changes that have seen travel to many more countries become easier and cheaper for passengers, progress we hope towards removing all test requirements for the fully vaccinated as soon as possible.
“However, it is disappointing for our customers to have no definitive clarity yet on when the lateral flow changes will be introduced.
“With the crucial October half-term just two weeks away we urgently need clarity so that passengers can plan ahead. This is the key booking period between now and Christmas, so time is of the essence.”
Before the UK's red list announcement, Paul Charles, chief executive of travel consultancy The PC Agency, had said that stripping the list down to just a handful of destinations would be a “a major step forward” as it meant the government was moving to a policy of “individual risk".
The removal from the red list of Mexico, South Africa and Thailand would send “a confidence boost across the sector and across consumers".
Mr Charles said it is “very hard to justify” why any countries are on the list “when there are no new variants of concern there".
The London-based World Travel and Tourism Council, which represents private companies, said the sector's recovery will continue to be “sluggish” due to policies such as the UK's red list.
The organisation predicted that travel and tourism's contribution to global gross domestic product is set to rise by less than a third in 2021.
On Wednesday, the UK government lifted its advice against non-essential travel to 32 countries and territories.
Bangladesh, Fiji, Gambia, Ghana and Malaysia were among the locations for which travel advice based on the risk of coronavirus has been relaxed, the Foreign, Commonwealth and Development Office said.
After the latest announcement, Health Secretary Sajid Javid said: “Our robust border measures have helped protect the phenomenal progress of our vaccination programme, and it is because of this success both here and around the world that we can safely open up travel further and we can visit friends and family abroad.
“We’re now making it easier and cheaper for people to travel by allowing fully vaccinated travellers from non-red list countries to use lateral flow tests on day two of arrival, as long as they provide proof of use.”