The two replace the creative director, David Prideaux, who quit in January to join Publicis Dialog, and Alison Meredith, who is taking a career break.
Fraser spent 15 years as a copywriter and creative part-ner at BMP DDB and joined DraftFCB as its executive creative director in 2006.
Fraser said: "I'll be sad to leave Nigel Jones and the team at FCB, but it was impossible to turn down the opportunity to play a leading role in one of the most admired independent agencies in the UK."
Griffin left Emap's Kiss FM in January after one year as the managing director. His agency career includes stints at Ogilvy & Mather and St Luke's. He joined Channel 4 in 1999, and rose to the position of head of marketing.