Parfitt will work alongside the region's senior management teams to help "nurture, shape and attract" the best talent.
He will work three days a week in the new post, alongside his advisory roles with BBC Radio and Comic Relief.
Parfitt, who left Radio 1 in July after heading it for 13 years, will report to Robert Senior, the EMEA chief executive of the SSF Group.
Senior said: "Andy has an extraordinary feel for creative organisations and their utter reliance on talent. And he understands talent like no other. He's unique and we're very lucky to have him on board."
Parfitt said: "I admire Robert's energy and insight enormously, and I am very excited to be part of this new challenge across such a diverse region.
"For me, Saatchi & Saatchi is the most famous creative agency in the world, making some great work with a range of interesting clients. There is a talented and collaborative senior team in place, and I'm really looking forward to the start of this new chapter."
Parfitt joined the BBC as a studio manager in 1980 and was part of the launch team for Radio 5 in 1990.
In addition to Radio 1, Parfitt headed the Asian Network and oversaw the launch of the digital station Radio 1Xtra. He also had the title of controller of popular music.
Parfitt was responsible for a revamp of Radio 1 and gave his backing to the station's breakfast DJ Chris Moyles despite controversy last year.