Kempe had joined the group in 2007 when it acquired JKL, the Nordics comms agency he founded in 1985. Since 2011, he has been based in London.
In a statement, MSLGroup chief executive Guillaume Herbette said: "Regarding Anders, this is a personal decision. He has decided to resign from his roles as president EMEA, JKL partner and member of the executive committee of MSLGroup.
"Anders will remain with MSLGroup as a senior adviser to our clients and colleagues for the rest of 2016. Anders' decision is unrelated to the integration initiatives at Publicis Groupe. Anders has explained that this is a well-considered decision and that, after 30 years in the industry, if he was going to do something different, the time is now.
"I really want to thank Anders for his many contributions over the course of the past few years, helping MSLGroup grow into one of the largest fully integrated marketing agencies in the world."
In January David Close, MD at MSLGroup in Boston, announced he was retiring from the agency after 22 years there and at its predecessor firms.