McCue, who been with the company for eight years, will replace Patrick Kennedy, who is stepping down at the end of the year. He currently oversees 3,000 staff and 2 billion euros (1.58 billion pounds) of turnover in retail and telephone operations.
Paddy Power Chairman Nigel Northridge credited McCue with "driving the company's regulatory agenda" and described him as a key member of the company's management committee.
Kennedy announced in May that he would step down after nearly 10 years in the role.
(Reporting by Conor Humphries; Editing by Pravin Char)
