The transaction is valued at $80m in cash.
Based in Winston-Salem, North Carolina, the display and packaging business specialises in point-of-purchase display design, manufacturing and fulfilment.
The business also offers contract packaging services for consumer product customers, with more than 250 brands.
It currently operates eight manufacturing and fulfilment facilities and four sales and design centres, employing around 450 people.
Last year, it produced net sales of around $135m.
Sonoco president and CEO Howard Coker said: “Our US Display and Packaging business has been an industry pioneer, with a legacy of providing innovative solutions for complex supply chain challenges.
“But Sonoco is focused on growing our core Consumer and Industrial packaging businesses around the world. By divesting this business, we expect to apply proceeds to further invest in ourselves while returning value to our shareholders.”
Rothschild and Co served as financial adviser for Sonoco during the transaction while Haynsworth Sinkler Boyd acted as legal adviser.
Based in Atlanta, Georgia, Hood Container is an integrated paperboard and speciality paper manufacturer specialising in containerboard, kraft paper, corrugated boxes, high-graphic displays and contract packaging, corrugated, folded box and displays.
In December, Sonoco divested its Europe contract packaging business to a subsidiary of Wisconsin-based contract packaging and contract manufacturing firm Prairie Industries Holdings for $120m in cash.
That month, the company also joined Holy Grail 2.0, a digital watermarks initiative to deliver on sustainability goals.
In August, Sonoco acquired France-based sustainable packaging company Can Packaging for €41.7m ($49.3m).
The deal was intended to expand Sonoco’s sustainable paperboard packaging offerings to various consumer food brands serving the European market.