The creative pitch will be handled by COI. A result is expected in September.
DDB London currently handles above-the-line advertising for the body, formerly known as the Teacher Training Agency. DraftFCB handles below-the-line duties; Manning Gottlieb OMD handles media planning.
The appointment follows an 8 per cent increase in funding by the Government for the TDA to increase its role in raising standards in schools.
A £770 million grant includes an extra £60 million to be spent on initiatives to recruit and train staff and modernise schools.
The brief will be to focus on TDA's dialogue with potential teaching candidates and make recommendations to support its strategic planning.
The body's most recent advertising centres on the enjoyment teachers get from the job, and runs with the line: "Use your head. Teach."