Karg will join the marketing analytics company at the beginning of 2016. Shannon Denton, the North America chief executive at Razorfish, will become the interim chief executive at Razorfish International from January.
Karg was named chief executive at Razorfish International, the Publicis Groupe agency, in 2013.
He was also the chairman across Razorfish and sister agency Digitas for the EMEA regions between 2011 and 2013. Karg took on the additional role after being named chief operating officer for Razorfish and Digitas International in 2010.
Karg began his career in the industry at Digitas as associate director for the digital strategy group in 2000.
Greenlees is stepping down after eight years, having decided that "now is the right time for new leadership to take the business to the next stage of its development".
He will remain on the board as an executive director for a handover period, and then work in an advisory role for two years from 30 April 2016.
A spokeswoman for Razorfish said that Karg will work with Denton and Alan Herrick, the chief executive at Publicis.Sapient "to ensure a smooth transition and continued growth of international clients and teams".
Michael Higgins, the chairman at Ebiquity, said: "Michael Karg is an outstanding appointment for Ebiquity.
"He has considerable experience across our industry particularly in digital marketing and in growing businesses on a global scale.
"He has amassed a wealth of international experience and has an impressive and proven track record in building marketing businesses. We welcome Michael.
"On behalf of the Board and the Company we are immensely grateful for Michael Greenlees’s vision, expertise and constant drive which have made Ebiquity the company it is today."