They will take their posts in November when Janet Lewis-Jones and John Taylor step down after ten years in the same posts.
Alison Hastings is a media consultant and a member of the BBC Trust and Chair of the Audience Council England and a veteran of the Press Complaints Commission.
Gerard Lemos is a Partner in Lemos and Crane Social Research and Visiting Professor in International Social Policy at Chongqing Business and Technology University, China. He is also deputy chair of the British Council.
Quentin Thomas, president of the BBFC said: 'The BBFC owes a debt of gratitude to Janet Lewis-Jones and Lord Taylor of Warwick for their dedication and wise counsel over the last ten years and I would like to thank them personally for their support and advice. They will be a hard act to follow, but I am confident that Alison Hastings and Gerard Lemos will bring a depth of highly relevant experience and expertise to the Board when they take up their posts in November. I am very much looking forward to working with them.'