In a PR career spanning 16 years, she also worked in the press office of the now-defunct Gillingham-based Thames Gateway NHS Trust and at Kent County Council.
At Medway she will head an eight-strong team that includes Darren Bindloss, the principal media officer, and marketing and PR manager Martin Reid.
She will report to Stephanie Goad, assistant director of comms and enterprise.
Glasson replaces Liz Dickens who left the council in March to become the London Fire and Emergency Planning Authority's first comms head.
Medway is currently involved in a PR initiative to promote the area to potential investors. This is through the Thames Gateway project involving local authorities surrounding the estuary as well as the Learning and Skills Council.
A major part of the campaign is handling publicity for a business conference in Chatham in June, titled Medway: The Future Unveiled.
Speakers at the conference include regeneration and planning minister and chairman of Thames Gateway Lord Falconer.
Glasson said: 'The promotion of regeneration was something that came over loud and clear during the interview. It's important that Medway is promoted nationally as well as locally. The area needs to be at the forefront of the minds of investors.'