Mr Breedon is currently chief executive of Legal and General but will step down from both his L&G and ABI roles at the end of June.
Mr Thiam will take up his part-time role at the ABI on 3 July. He has worked at Prudential, a sponsor of the Institute of Financial Planning, since 2008 and previously worked at Aviva. His ABI role will be in addition to his role at Prudential.
He said: "I am honoured to be chosen as chairman of the ABI, particularly in succession to Tim Breedon who has done an outstanding job in refocusing the organisation to face the challenges of a changing world.
"Insurers need to continue working together in close partnership with government and regulators to find solutions to the challenges we collectively face - supporting our customers in a time of unprecedented austerity and developing practical polices that will promote sustainable growth."
Otto Thoresen, director general of the ABI, said: "Tidjane Thiam is a globally-recognised business leader whose understanding of the opportunities and challenges facing the global insurance industry will be a huge asset to UK-based insurers.
"Tim has refocused and re-energised the ABI and has played a key role in both the public leadership of the UK industry and ensuring the ABI is equipped with the strategic direction, consumer perspective, member engagement and key staff to deliver for its members in this challenging environment."