Burstow joins ex-home secretary Charles Clarke and former BIS and Defra permanent secretary Sir Brian Bender, who already work for the agency.
The former MP is currently leading the Right Place, Right Time Commission for NHS Providers examining transfers of care. His primary role at MHP will involve working with the firm’s health practice, supporting thought leadership and marketing activity as well as giving counsel to clients.
MHP CEO Gavin Devine said the appointment adds another layer of expertise to the firm.
He said: "I am very proud that well-respected people like Paul want to work with MHP, which is a testament to the company's superb reputation."