In opting for King, a close ally of Perriss, ZenithOptimedia's parent, Publicis Groupe, has scotched rumours that it would turn to the sister network Starcom MediaVest Group to fill the vacancy.
Reports in the US that Rich Hamilton, ZenithOptimedia's chief executive in North America, would succeed Perriss also proved unfounded.
King, 44, was one of the founding directors of Zenith Media alongside Perriss and has occupied various local and international roles since.
His elevation follows Perriss' decision to retire from day-to-day management responsibilities. Perriss will look to take a small number of non-executive roles once he has left ZenithOptimedia.
Perriss said: "I am delighted Steve is to take on my role. As well as being highly regarded and respected throughout the ZenithOptimedia global network, with a reputation for effective client service, Steve is also a very charismatic and personable leader."
After becoming the managing director of Zenith Media in the UK in 1993, King moved to the US in 1994 to work on the launch of Zenith there and in 1996 became the chief operating officer of the US business. He took on a European role for Zenith in 1997 and took the enlarged EMEA chief executive role when ZenithOptimedia was created in 2001.
King said: "I'm obviously delighted and eager to meet the challenges of this position. John has helped this company achieve tremendous momentum, and I share his determination to preserve and enhance ZenithOptimedia's status."
Publicis also said that it remained committed to preserving the ZenithOptimedia and Starcom MediaVest brands. Roger Haupt, the president and chief operating officer of Publicis Groupe, said: "We need strong leadership at the top of both organisations as we continue to strengthen each network."
ZenithOptimedia is the world's sixth-largest media network with billings of $16 billion. Key clients include Mars, SC Johnson and Toyota.