Bank of New York Mellon Corp., the world’s largest custody bank, said Robert P. Kelly stepped down as chairman and chief executive officer because of differences with directors in his approach to managing the company.

Gerald L. Hassell, Mellon’s president, was named Kelly’s successor, the bank said Wednesday in a statement. Kelly, 57, had led the company since 2007. Hassell, 59, has been with Bank of New York for more than three decades, according to the statement.