The two facilities, which are primarily involved in the production of unprinted films for the meat and fish processing industries, are based in Lund, southern Sweden, and Somerset, south-west England.
The companies will be sold to Swedish private equity group Accent Equity for an undisclosed sum.
New angle Amcor spokeswoman Liesl Weber told FoodProductionDaily.com that the two businesses would be run as a single operation under some members of the existing management team, as they have been doing for some time.
"This sale is seen as a very exciting development for these businesses," she said.
"The new owners have a new angle and new ideas for growing the business."
"It is no longer a core business for us, but the new owners see very positive opportunities for these two companies."
"For Amcor, we can now take the money from the sale of these units and reinvest in improving our core businesses, areas where we feel we can grow the company."
This is likely to include stepping up operations in lower-cost areas such as southern and eastern Europe, as well as increasing investment in research and development.
Investments & restructuring The company has already announced an investment of €25m in the Polish town of Lodz, as well as another new Polish facility that will supply packaging for PepsiCo's snack food business in eastern Europe.
Amcor is hoping to make pre-tax cost savings of around €30m this year as a result of its restructuring.
The aim is to move out of basic packaging materials such as the unprinted films produced by the Swedish and British plants and to concentrate on sectors with higher added value, such as finished flexible packaging.
When Amcor, which has 38 manufacturing plants in 15 European countries, first announced its European restructuring a year ago, it warned that western Europe would take an increasingly small share of its business in the years to come: the region will account for just 20 per cent of sales in 2009, compared to 32 per cent in 2005.
In contrast, eastern Europe will account for 20 per cent of Amcor's revenues in 2009, compared to just 12 per cent in 2005, as a result of increasing demand for new food and drink products.
Costs are also playing a part in the decision to shift focus - while there will still be some growth in western European markets, Amcor said it could not afford the levels of investment needed to meet all this potential, and that the money could be better spent in other parts of Europe.
Last year the company sold its PET packaging business to Spain's La Seda de Barcelona for €425m as part of its withdrawal from the plastic bottle market in western Europe.