His role at the BRC replaces the head of PR role and includes board status, heading a 19-strong team and reporting to CEO Sir Nicholas Young.
Beaver will head all press, PR, marketing, campaigns, internal communications, publications, online activity and archiving.
For the past three months, consultant Charles Anson, a former Royal press secretary, filled the comms director post as an interim measure.
Beaver said: 'As a priest, I am concerned about the dignity of people and poverty issues and the Red Cross symbolises the action being taken to meet that challenge.'
CE is reviewing its PR function with a view to a restructure later this year.
Steve Jenkins, currently head of media relations, will head communications in the interim.