US Defence Secretary Chuck Hagel said the Americans will leave RAF Mildenhall in Suffolk and RAF Alconbury and RAF Molesworth in Cambridgeshire.
The move is part of a programme to save £320m ($500m) a year across Europe. The USAF lease the RAF bases.Mr Hagel said he understood it would mean job losses and thanked those who had supported the US Air Force.
“I know that this will result in a reduction of our local host nations workforces at some locations; I value the tremendous support they provided us for decades.”
The USAF KC-135 tanker fleet based at Mildenhall will be moved to Germany.
RAF Lakenheath, with two squadrons of new F-35 jets (48 of them) arriving by 2020, will be the aircraft's only European base.
The Pentagon said the loss of about 2,000 US military and civilian personnel is due to relocation away from Mildenhall, but will be offset by the addition of about 1,200 people stationed permanently at Lakenheath.
Matthew Hancock, West Suffolk MP and Minister of State for Business, Enterprise and Energy, said he would support the community affected.
Mildenhall had a long and proud history of strong relations with the United States Air Force and the move “will come as a shock to many”, he said.
“I have met with the defence secretary, and others in government to ensure we can work, together with the American administration, to support the community.
“We will create a Mildenhall, Alconbury and Molesworth (MAM) Working Group, which I will chair, inviting local LEPs [local enterprise partnerships], councils, the Ministry of Defence and US representatives to ensure no stone is left unturned in supporting Mildenhall and the surrounding area.”
A UK Ministry of Defence spokesman said: “The US Department of Defence (DoD) has been reviewing its requirement for bases across Europe as part of (its) European infrastructure consolidation review.”
RAF Mildenhall is used as a transport hub by the USAF and is home to air refuelling tankers and special operations forces.
It has about 3,200 military personnel, with 400-500 UK civilian staff employed there.
Both bases are in the Forest Heath District Council area.
James Waters, leader of the council, said: “The USAF contributes significantly to the local economy so the expansion of RAF Lakenheath, and with it the US government's commitment to the site as part of its long term plans, is very welcome.
“But this happiness is obviously tempered by our sadness that Mildenhall is to close.
“Both announcements mean huge changes to the landscape of Forest Heath , but I am optimistic that with every change there are opportunities for reinvention, growth and investment.”
By Jonathan Marcus, BBC Defence and Diplomatic Correspondent
For some years now the US military has been reviewing its bases in Europe, eager to reduce its footprint to rationalise and cut costs.
In part it is due to budget constraints but it is also driven by strategic changes as the Pentagon turns its gaze increasingly towards the Asia-Pacific.
RAF Mildenhall has been an important base for the Americans since the early 1950s when it was home to strategic bombers.
Currently it houses US Air Force Special Forces and a fleet of air-to-air tankers.
The latter, though less glamorous than fast jets, are some of the most important elements of the USAF, described by one analyst as the “kryptonite” of modern air power.
They enable combat and support aircraft to reach their targets and to remain over combat zones for the time needed to carry out their missions.
It is likely that the KC-135 tankers from Mildenhall will move to a US base in Germany.
British defence sources are eager to stress that the base closures here – two US-run communications stations at RAF Alconbury and RAF Molesworth in Cambridgeshire are also to shut down – do not represent any dilution of Washington's commitment to European security.
Indeed RAF Lakenheath is due to host two squadrons of new F-35 aircraft when they enter service.
Over recent months the Americans have deployed small but significant reinforcements to Europe to reassure NATO allies like Poland and the Baltic republics in the wake of Russia's actions against Ukraine.
The US had hundreds of tanks in Europe during Cold War but there was a brief moment after 2013 when all US tanks had been withdrawn from Europe.
Today about a battalion's worth are back in Europe exercising with allies.
But the Pentagon has plans to store an armoured brigade's worth of equipment – some 150 tanks along with other armoured vehicles – in Europe by 2015.
RAF Alconbury and RAF Molesworth are used as USAF communications bases, rather than for flying, and their operations were expected to move to RAF Croughton in Northamptonshire.
The USAF has about 750 military personnel at the two Cambridgeshire bases, with a further 1,500 civilian employees and dependents.
Jason Ablewhite, leader of Huntingdonshire District Council, said the news was “hugely disappointing” as both bases contributed about £40m a year to the local economy.
He said it would mean the loss of 760 personnel and 1,500 civilian jobs, adding: “The impact on the local economy could be considerable.
“However, the Enterprise Zone is on the same site as RAF Alconbury, and will provide thousands of jobs over the coming years.”