Mead, who is also GA's global head of the Americas and head of the firm's US operations, is leaving after seven years to join Brunswick's New York office in the autumn.
He is to focus primarily on corporate issues and crisis management.
Mead joined GA in 1998 after nine years at Sawyer Miller Consulting where he was most recently president.
GA MD Montieth Illingworth will take over the New York office from Mead. No new president has been named.