She joins as an associate director from the Cabinet Office (CO) where she was special advisor to Baroness Jay, former leader of the House of Lords and minister for women, since 1998.
Gibbons decided to move into consultancy work after Jay's retirement from frontline politics following the general election.
Her appointment has brought the public affairs team staff level up to six. She reports to public affairs director Bernard Hughes.
Gibbons said: 'I had considered staying on within Government, but felt I wanted to try something else where I could use my knowledge in a different way.'
Before advising Baroness Jay - who is being widely linked in media reports with the chairmanship of the BBC's board of governors - Gibbons was a PRO with the Football Association. There she worked on its failed attempt to bring the World Cup to England in 2006.
She worked in PR for the Labour Party at Millbank and for white collar trade union MSF before that.
* Edelman has been appointed to the pan-European corporate and financial PR brief for mortgage company PMI Group, winning a year's contract after a three-way pitch.
Director Claire Corrie leads a four-strong team reporting to PMI Group global PR head Kristin Chen and UK MD Gunnar Lindh. Edelman first worked with the US-based client on its European and UK launch in February.