Sir Chris, DHSC permanent secretary since 2016, will take up his new role as Cabinet secretary on 16 December.
The role is the most senior civil service adviser to the prime minister and cabinet, as well as the head of the civil service.
Prime minister Sir Keir Starmer said Sir Chris would deliver 'mission-led government', including 'the complete re-wiring of the British state to deliver bold and ambitious long-term reform'.
The current chief medical officer, Sir Chris Whitty, will oversee management of the department until a permanent replacement is chosen. He has been chief medical officer since 2021 and was previously chief scientific adviser to the DHSC from 2016.
Former Leeds City Council chief Tom Riordan joined the department in the role of second permanent secretary in September.
It comes as the DHSC also needs to select a new chair of NHS England – with Richard Meddings standing down in March – and of the Care Quality Commission, whose current chair will also leave in March.