Following the changes Mark Goodwin, Jason Lawes, Sam Ball and Dave Bedwood will jointly run the creative department at the agency as creative directors. Grant Parker will continue in his role as head of art.
The restructure follows the appointment of Tom Bazeley as the chief executive of M&C Saatchi in October. Bazeley was previously a founding partner at Lean Mean Fighting Machine, which M&C Saatchi bought in May 2014.
Bazeley said: "We are re-looking at how the whole agency is structured and putting the creative integrity of our work right at the heart of that.
"In a communications world where ideas can come in many shapes and sizes. I want the person making the ultimate creative decisions to be deeply involved in the account.
"They will need the time and space to understand the business challenges, provide inspiration, write ideas, encourage innovation, nurture people and deliver smart, brilliant and newsworthy ideas.
"Having one person working at a very high level isn’t the way to achieve this."
As the creative directors will have "autonomy" over their clients’ work, there is no need for an executive creative director across the group.
Lynn was hired as executive creative director in February 2012 from Profero, where she was in the same role from 2009. She replaced Graham Fink, who had moved to Ogilvy & Mather China.
Lisa Thomas, the group chief executive at M&C Saatchi, said: "Elspeth has overseen some fantastic work but as a result of the restructure she and I agreed that it was time for her to leave the agency.
"We thank her for her obvious passion and dedication to the agency and our clients and for helping us to modernise the agency. She is a unique individual who will be greatly missed."