The two plants, with a combined workforce of over 370, had sales of 42m last year. Amcors nine existing UK manufacturing sites turned over 150m.
An Amcor spokeswoman said it was too early to determine the plans for the sites, although European chief executive Graham James revealed that the Thetford plant would be known as Amcor Flexibles Camvac.
Thetford specialises in high barrier vacuum metallising and coating, while Ledbury operates in the bakery and produce markets.
Rexam said the disposal would "sharpen" its focus on medical packaging and the pharmaceutical and personal care sectors.
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