But the US has named RAF Lakenheath to be the first permanent European base for the F-35 aircraft.
The US currently has more than 60,000 troops stationed in Europe, mostly in Germany, Italy and the UK.
The number will remain the same, as the US ramps up rotations within Europe for training programmes.
Many of the closures affect smaller bases that were remnants of the Cold War.
But US officials also have finalised plans to cut about 500 military personnel from the Lajes military base in the Azores islands, which drew opposition from Portugal.
The changes will mean a net reduction of about 2,000 US personnel in the UK over the next several years.
In the UK, the US Air Force will leave RAF Mildenhall in Suffolk and RAF Alconbury and RAF Molesworth in Cambridgeshire.
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."
Other countries with closing bases include Germany, Belgium, the Netherlands and Italy.
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.
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