In his new position, Marsh will be responsible for working with clients including Barclays, Somerfield, Cancer Research UK and Legal & General. He will also be in charge of helping to further develop the agency's capabilities in the digital field.
Marco Scognamiglio, the Rapp group chief executive, said: "Bringing Russell in is a logical next step in the development of our digital expertise. He will be a key member of the management board as we put in place all the skills necessary to help navigate our clients through the changing consumer landscape."
Marsh left Agency.com in July. Before joining the Omnicom-owned agency, he worked for four years as a director at Fullsix.
Marsh said: "I'm looking forward to helping Rapp build on its market-leading platform and ensuring its digital expertise is seen as 'best in class'."