Smurfit is the grandson of Jefferson Smurfit, who launched the company in Dublin in 1938. He replaces previous boss Gary McCann.
McCann, who announced his retirement in May, was appointed chairman of Paddy Power in July. He joined the bookmaker as a non-exec in November 2014.
SKG chair Liam O’Mahony said: “The board would like to thank Gary for his substantial contribution in leading the group over the last 13 years and wishes him well in his retirement.”
He added: “The board looks forward to the group’s next phase of growth and development under Tony’s leadership.”
Smurfit Kappa operates across approximately 350 production sites in 12 countries in Europe, and another 12 in the Americas. The group employs around 43,000 people worldwide.
Earlier this year, it was reported that US-based International Paper was weighing up a £6bn offer for Smurfit Kappa. However, the Dublin-based group declined to comment on the speculation.
Smurfit Kappa reported revenue of €4bn (£2.94bn) in the first half of 2015, up one per cent from the €3.95bn in the same period of last year. Profit before tax was up seven per cent, from €62.3m in the first six months of 2014 to €73.2m.