The deal gives the whole of IMA an enterprise value of between 6.5 billion and 7 billion euros ($7.2 billion-7.7 billion), two sources close to the matter said. Earlier a third source said it was around 6.5 billion euros.

BC Partners' stake was worth around 45% of the company, one of the sources said.

Italy's Vacchi family will remain the majority owner of IMA, the company said in a statement.

"We believe BDT & MSD's long-term view and deep expertise in supporting family enterprises makes it an ideal partner to help us ... accelerate global growth, including in the U.S. market," IMA's Chairman and CEO Alberto Vacchi said in the statement.

IMA is interested in growing in the United States, both organically and through an M&A deal, two sources told Reuters.

In May BDT & MSD Partners, the advisory and investment firm run by former Goldman Sachs banker Byron Trott, said it entered into a definitive agreement to acquire a significant stake in U.S. packaging solutions provider ProMach alongside the existing majority owner.

The sale of IMA's stake comes just two and a half years after BC Partners partnered with the Vacchi family to take the company private from the Milan stock exchange. At that time IMA's equity value stood at just less than 3 billion euros.

In the deal announced on Monday, Poggi & Associati acted as lead financial advisor. Mediobanca and BofA Securities also acted as financial advisor to IMA. JPMorgan Chase & Co. provided financial advice to BC Partners.

(Reporting by Elisa Anzolin and Gianluca Semeraro, editing by Alvise Armellini and Susan Fenton)