Rhodes joins the agency this month from Wunderman, where he was responsible for leading the agency's Best Buy business.
In his new role, Rhodes will be responsible for handling Iris's relationship with Barclaycard.
Prior to Wunderman, Rhodes was managing partner at Proximity London and deputy managing director at now-defunct Craik Jones Watson Mitchell Voelkel.
Ian Millner, chief executive at Iris, said: "Agencies tend to get the clients they deserve. We believe in client partnerships, and we believe in investing in these relationships so that we can continue to add value to their business.
"We simply need to have the best, the most ambitious and open-minded talent there is. Graham is a great addition to our team and we're really looking forward to getting stuck in."
Rhodes said: "I wanted to join a forward-looking creative business, which constantly uncovers the most powerful insights and produces the best and most envious work – work that drives commercial gain, and, ultimately, work clients love and consumers want to talk about."
Iris's clients include Sony Ericsson, Orange, Locog, Philips, Adidas, Wonderbra, the FA, Volkswagen and Shell.