Richardson will lead the public affairs team and handle strategy and thought leadership for the exploration and production arm of the power giant Centrica, which is a separate division from electricity and gas retail business British Gas.
Centrica devolved its centralised public affairs operation to the company’s individual businesses last September.
Centrica Energy's corporate affairs director Gabe Winn said that, previously, its public affairs was UK-focused, but that there had been an increasing need to take a more international approach, which will now form part of Richardson’s focus.
Commenting on the role, which she takes up on 8 September, Richardson said: "Delivering the UK’s energy security in a clean and affordable way is one of the defining challenges of my generation. It will be a privilege to play a part in helping to communicate the issues and solutions for this complex and vital industry."
In her current role at Edelman, Richardson has provided senior counsel for chief executives and global brands, including Unilever, Shell and Roche.
Edelman Public Affairs MD Gurpreet Brar said: "We wish Sarah all the best as she takes on this exciting challenge." The agency is expected to make a number of public affairs hires later this year.
Before joining Edelman, Richardson, who is married to the Conservative MP Damian Collins, was a journalist for the London Evening Standard for 14 years.
She also served as a Conservative councillor on Westminster Council for 12 years until May this year. During her political career she was the cabinet member for children’s services and also served as Lord Mayor of Westminster, the youngest woman ever to hold the office.
Earlier in her career Richardson worked in the US Congress as an aide to Dick Gephardt when he was minority leader of the house, and has also spent time on secondment to Starbucks as director of external affairs during its recent corporation tax controversy.
Winn told PR Week that the energy industry "needs to communicate better across all stakeholder groups".
He added: "As well as a successful Westminster and media career, Sarah has a wealth of real-world experience tackling some of the biggest issues facing global businesses. Her insight and experience will bring additional strength to our public affairs team and will play a valuable role in how we approach our communication challenges."