The UK-based firm said that it expected the deal to be completed during the second quarter of 2012, subject to approval from European antitrust authorities. The acquisition was unveiled last month.
DS Smith will buy the entire packaging operations of Sweden-based SCA, excluding two Kraftliner mills.
Employment law in France means it has to apply to national authorities for the French assets. DS Smith confirmed the formal offer had been submitted.
Company chief executive Miles Roberts Friday said he was “delighted” with the result of the vote and that the focus would remain on the strategy to integrate both firms.