Mr Driscoll has more than three decades of experience in media and marketing.
He announced his departure from communications agency Marketforce last week, where he is CEO and chairman. Mr Driscoll will complete his tenure at the company in September.
Alongside his new role, Mr Driscoll will continue as chairman of Rottnest Island Authority and Trinity College, and as deputy chairman of the Wheelchair Sports Association WA.
Former WA chief executive Chris Wharton retired in March after taking extended leave in 2016, ending more than 20 years with the company.