Edwards was previously deputy comms director at the organisation. Revill has left to become CEO of the British Society for Immunology.
Richard Scanlon, CEO of the Royal College of Surgeons, said: "I am pleased to welcome Simon to this post. His experience and knowledge will stand the college in good stead as we approach the general election.
"This appointment underlines the importance of communications at this crucial time for surgery in the recent health reforms. I also thank Jo Revill for her contribution to the college and wish her every success for the future."
Prior to joining the Royal College of Surgeons in 2008, Edwards led the biosciences and health policy team at the Royal Society.