Turner was previously a creative director at JWT and most recently was at Mather Communications, part of the Ogilvy Group. He takes over from Hayter, who left the agency last week to join The Gate.
Turner has recently worked on clients including Deutsche Bank, Credit Suisse and Barclays Wealth.
Jo Parker, chief executive of Teamspirit said: "At a time of unprecedented turmoil in the financial services marketplace, Geoff's creative flair and experience will be worth its weight in gold.
"It is also important for us to bring in someone who just doesn't think in advertising terms, but shares our belief in the power of integrated communications."
Teamspirit's clients include Prudential, Abbey for Intermediaries, Aviva and Aegon Asset Management.