Muir has been made group director of corporate affairs at the London-based facility, which is one of 275 nationwide owned by The Priory Group and working in the fields of mental health and addiction.
Muir, who will report into Priory Group CEO Tom Riall, was head of comms at Circle Partnership and was previously a senior political adviser at Conservative Campaign Headquarters.
His move comes as The Priory seeks to build its in-house PR team, with two more hires expected shortly.
He said: "It's a fascinating time for the group and I'm delighted to be joining to help develop this world-leading brand further."
Circle Partnership, which runs hospitals across England and manages Hichingbrooke, the first franchise of an NHS hospital, has appointed Gordon Hector as head of comms.
Hector was a senior speechwriter at the Department for Education and was previously head of public affairs for the social policy charity Joseph Rowntree Foundation.