Grant was promoted to control Capital's national sales operation in May and previously held the position that Miller will fill.
Miller's task is to take charge of all marketing, communications, research and creative development supporting Capital's dealings with advertisers, sponsors and agencies.
He will help to raise the commercial profile of brands including Capital FM, Capital Gold, Century and Xfm.
Having joined Starcom in February 2002 to head its Honda, T-Mobile and Nectar accounts, Miller has also worked at BMP DDB and Saatchi & Saatchi in China and filled the role of head of media marketing at BAA.
Miller is one of three directors who will report to Grant. The others are Mike Hope-Milne, the former MediaCom head of radio, who was recently promoted to brand sales director at Capital, and a yet-to-be-appointed group sales director.
Grant said: "Gavin shares my vision that the most fruitful way for media businesses to build relationships with advertisers is to behave like true brands themselves. Gavin brings a wealth of experience to the job having had senior retailer and market development roles and having been a media buying client and media agency practitioner."