Prospect had been pressing the company to appoint a worker representative to Openreach's new board.
Brendan worked for the Trades Union Congress for many years and retired in 2012 after serving as TUC general secretary for nine years.
He is currently chair of the Advisory, Conciliation and Arbitration Service (ACAS).
Prospect negotiator Philippa Childs said: "We are absolutely delighted with this appointment. Brendan will bring a wealth of experience of industrial and employee relations to the Openreach board.
"We very much look forward to working with him."