The UK-based firm said Johnson, who also resigned from the board, had been planning to retire in 2012.
Davis, who has been acting chairman since October 2011 and has been a non-Executive Director of DS Smith Plc since June 2010. He will become Chairman of the Board and of the Nominations Committee, said a company statement.
Previously, he was Group Chief Executive of Imperial Tobacco PLC and is Chairman of both Wolseley plc and William Hill PLC.
Chris Bunker, senior non-executive director of DS Smith, said: “On behalf of the Board and the Company, I would like to thank Peter for his immeasurable contribution to DS Smith. He has led the business through a period of transformation, and the business is in an excellent position to grow and develop further as a result.”