The defence secretary's announcement comes after months of criticism over the number of helicopters in operation in Helmand, Afghanistan.
In total, the Chinook fleet will increase in size from 48 to 70.
But the money will have to come out of the Ministry of Defence's existing budget, which is already overspent.
Mr Ainsworth said: "Helicopter capability has already doubled in the last three years and this future strategy builds on this, ensuring that our armed forces have the very best resources at their disposal."
RAF Cottesmore opened in 1938 and during the 1960s was the base for nuclear capable Vulcan bombers.
It has been home to Harriers since 1999 and these have recently served in Afghanistan.
The planes were developed in the early 1960s and had been due leave service in 2018 but this is now likely to be brought forward.
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