Averill most recently worked as deputy director of the British Board of Film Classification and previously worked at UKTV.
She succeeds Jane Cussons as chief executive and officially takes up her post this month. She will report to WFTV chair Sophie Balhetchet.
Averill said: 'I've known Sophie for many years and her work as a producer where she's created strong leading roles for women. When she offered me the opportunity to head Women in Film and Television I jumped at the chance.'
Balhetchet added: 'Penny combines experience with energy; humour with thoughtfulness. Above all she wants to build WFTV into an organisation that speaks to, and involves young women. We are delighted to have a woman of such calibre at the helm.'