The Berkshire-based packaging group, whose bid to acquire SCA Packaging was approved by regulators in May after it agreed to sell three production plants in the UK and France, aims to become the leading supplier of recycled packaging for consumer goods in Europe.
DS Smith believes the acquisition will provide access to new markets across continental Europe.
Chief executive Miles Roberts said: "The SCA Packaging business is very complementary to DS Smith’s strengths and creates a significantly enlarged geographic footprint.
"Together, we are now better positioned to meet the needs of our pan-European customers, deliver higher standards of customer service and drive forward product innovation.
"We can now start to integrate, develop and grow these two excellent businesses as we look to deliver substantial value for our customers, shareholders and employees."
DS Smith has more than 10,000 staff at 94 manufacturing sites while SCA Packaging employs around 12,600 people at 110 different sites in 21 countries.