The agency has promoted Susan Gilchrist to group chief executive and Rob Pinker to chief operating officer. Gilchrist is based in New York, while Pinker is based in London and Johannesburg.
Gilchrist joined Brunswick in 1995 and relocated from London to New York in April 2010 to head up the agency's US operations.
Both will report directly to executive chairman Parker. According to a statement issued by the group, Parker 'will be freed up to take on increasing external and client-facing roles'.
Brunswick has not had a group chief executive since former Ofcom CEO Stephen Carter, who left in 2008 to work in Gordon Brown's government.