The WPP agency won the business after a four-way pitch against incumbent Manning Gottlieb, Omnicom agency PHD and independent Naked.
The review, run through COI, also involved a creative pitch, won by incumbent advertising agency DDB London.
TDA, formerly known as the Teacher Training Agency, was set up in September 2005 to raise standards in schools.
The body's most recent advertising uses the line: "Use your head. Teach."