Grayling had held the account for several years. It was led by director Nicky Hughes, who quit to become head of PA at London 2012 (PRWeek, 11 August).
CRG chair, BSkyB corporate responsibility director Ben Stimson, said Geronimo's contract would start on 1 October.
CRG is made up of around 80 UK firms including AOL, KPMG, Kellogg's, Prudential and National Grid.
The group also provides professional development services for members.