The position will see Mrs Briginshaw, who has also served as head of design for the Department for Children, Schools and Families, take responsibility for the strategic lead of all design and sustainability projects.
She will also develop a national strategy to ensure that the HCA delivers quality housing at a low cost.
Mrs Briginshaw said: “There are few higher-profile and more critically important roles than pushing forward the sustainability agenda, in delivering new homes and regenerating places, and I am looking forward to being part of a core team that will be at the forefront of this.
“Both Partnerships for Schools and the Department for Children, Schools and Families have been fantastic places to work and I am grateful for the tremendous support I received from colleagues there.
“I am relishing the opportunity to further develop my passion for quality design and its contribution to creating sustainable places, in new challenges at the HCA.”
Mrs Briginshaw is due to take up her new post on 19 April.