Based in the London office, Hagger will be responsible for the day-to-day running of the agency when she starts on 5 June. She will work closely with head of client services Lizzie Snell and report to UK chief executive Neil Miller.
Possible has created the role of managing director to allow Miller to "focus on key accounts, new-business development and agency growth".
Before Google, Hagger was head of digital and technology at The Lighthouse Company. She was chief marketing officer at SapientNitro (now SapientRazorfish) EMEA between 2012 and 2013, and was briefly head of digital at AAR in 2012.
Hagger spent 11 years at Glue London (now Isobar UK) from 2000 in roles including managing director and chief integration officer.