Edwards, director of the Active Communities Directorate since 2002, has been appointed director-general of the Home Office Communities Group.
She will be responsible for the Home Office's work on active communities, civil renewal, race equality, faith and community cohesion. She will also handle the politically contentious subject of identity cards.
Edwards' new job is one of several high-profile sector appointments to be announced in the past week. Mark Curtis, the former head of global advocacy at Christian Aid and a controversial critic of British foreign policy, has been named as the new director of campaigning organisation the World Development Movement. He will start in June.
David Parsons, chairman of WDM's governing council, said: "Mark is dedicated to the radical grass-roots activism for which WDM is famous. His commitment to speaking the truth to those in power, no matter how uncomfortable, makes him ideal to take WDM forward."
Curtis has recently criticised the UK's development charities for being too close to government.
"I think most supporters of NGOs would be horrified by the degree to which they are co-opted by the powerful," he told Third Sector in September.
The first director of ActionAid UK, part of the newly formed ActionAid International, has been appointed. Richard Miller has spent the past 17 years working for Cafod, most recently as regional representative for Africa, based in Zimbabwe.