The organisation lobbies on behalf of the industry and also appears in the media to represent the financial services industry.
Browne takes over from Angela Knight, who said in April she would step down following a five year spell as head cheerleader for Britain's banks.
Anthony Browne said: “It will be an honour to lead the BBA, helping to resolve the complex issues still surrounding banking five years after the start of the financial crisis. We need to continue to lead on reform, ensuring the banking sector meets the needs and expectations of our customers and shareholders, and can play its pivotal role in returning the UK to economic growth.
"In a time of change and uncertainty, the BBA has a critically important mission to ensure the banking sector returns to health, remains in Britain, and has the trust of the public and politicians.”