The union Unite has blamed government defence cuts for the closure, which will mean 378 job losses.
The company, which employs about 800 people at Ansty, said it hopes to avoid compulsory redundancies.
Unite national officer for aerospace and shipbuilding, Ian Waddell, says: "The underlying reason for the job losses is the government's defence spending cuts."
A spokesperson for Rolls-Royce said: "We are in consultation with trade unions over reductions in our defence workforce at Ansty.
"We hope to achieve this without compulsory redundancies.
"In a large and complex company there is a continuing need to align resource and customer demand."
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