PRWeek understands the move is a result of internal changes and she will not be replaced.
She has been in the role since May last year after taking over from her predecessor Alan Oliver, and was responsible for managing an external relations team of 18 people.
Joseph is a former journalist, press secretary to Tony Blair and the architect of the This Girl Can campaign while at Sport England.
She has previously worked as managing director of public affairs at Grayling and as a consultant for several years.
It has been reported Joseph will "rekindle" her brand consultancy, which she founded in 2011.