Creative director Frederik Anderson has transferred to Story's New York office.
Formerly the executive creative director at IMG, Alexandrou will oversee Story's European creative team.
Geoghegan has been drafted in from Media Square where he was a marketing board director at Wax Communications. His new role will see him responsible for strategic growth across a variety of sectors along with the development of the Story brand in the UK.
Alexandrou said: "What attracted me most is Story's fundamental appreciation for the role of brands as media creators, not just consumers."
It has a portfolio including Empire Cinemas and clothing brand Oasis.
, a cloud-based email provider, and will oversee the reengineering of its brand.