Corkey, who was assistant director of comms and strategy at the council, landed the job ahead of external candidates after a selection process concluded last week.
She had been working in the role on an interim basis since Alex Aiken left earlier this year to become executive director of government comms.
Corkey first joined the council in 1998 to help look after its millennium programme and has since worked with both the comms and policy teams.
She said: ‘I have a strong team and strong foundations left by Alex, and now I want to build on those. Key to moving forward will be driving digital work and delivering comms in a way most convenient to our residents.’