Daley joins the authority next week as chief operating officer, reporting to HPA director of communications Lis Biranne.
At GSK, Daley leaves behind a five-strong team under the leadership of head of external comms Kate Hewer, who returned from maternity leave this year.
Before GSK, which he joined in 2004, Daley worked as a press officer at the Department of Health.
Last month, GSK warned of job losses as it announced cost-cutting plans to offset falling sales of diabetes treatment Avandia. Sales have declined since a study concluded that it increased the risk of heart problems.
The pharma firm is aiming to save £700m in annual costs within three years.
‘The move is a great opportunity at a time when public health is high on the media agenda,’ said Daley of his HPA appointment.
The HPA gives advice to the NHS, local authorities and the emergency services.