Health secretary Jeremy Miles confirmed the news after pre-appointment hearings by the Senedd's Health and Social Care Committee on 3 July.
Williams, who has been vice-chair of Powys Teaching Health Board since 2022, will take up her new role from 1 October 2025.
She said: ‘Over the past three-and-a-half years I have been inspired every day by the dedication of the staff, who continually strive to offer the very best service for local people, I am grateful to each and every one of them.'