The agency will look to Marsh to further develop its digital expertise, according to Marco Scognamiglio, Rapp group chief executive.
"Russell will be engaging with clients at the most senior level, articulating our integrated approach to communications planning, leading and motivating our digital talent across the group and playing a key role in helping us develop new proprietary tools."
At Rapp's sister shop Agency.com, Marsh was the senior point of contact for all Omnicom agencies working with Procter & Gamble across Europe, Middle East & Africa. He rose to managing director from head of client services.
He left the agency in July without a job to go to and will join Rapp next month.
Rapp (formerly WWAV Rapp Collins) works for clients including Barclays, Somerfield, Scottish & Newcastle, Pfizer and Legal & General.