Rainey, Kelly, Robert Campbell and Mark Roalfe completed their earn-out period a year ago. The four sold their eponymous agency to WPP for £27 million in 1999. The founders received their final payment last month.
Rainey and Kelly will stay on as the agency's chairman and chief executive respectively until April. It is unclear what the pair will do subsequently, although it is known that RKCR/Y&R's WPP parent is keen to find alternative roles to suit them.
The news leaves Roalfe, the executive creative director, as the last remaining founder at the agency, following the departure last year of Campbell to McCann Erickson to be its executive creative director.
Roalfe is expected to be named as chairman over the coming weeks, while James Murphy, the managing director, is in the running for the chief executive title.
David Golding, who was brought in as the planning director last year, is likely to become the executive planning director.
Likewise, the creative director Ben Priest, who joined at the start of this year, is likely to become the executive creative director.
The reorganisation was part of Y&R's succession management programme designed to reduce the impact of the founders' departures on the agency's clients.
William Eccleshare, the chairman and chief executive of Young & Rubicam, EMEA, refused to confirm RKCR/Y&R's succession plans, saying they would be announced next week.
However, he said: "MT and Jim have performed a flawless textbook exercise in managing the launch of an agency, building it to the highest levels of respect and success, merging it seamlessly into a major network and then developing the next generation of management. They are both great agency leaders and we shall miss them, of course, but they will leave with our ultimate admiration and thanks."
Before setting up RKCR, Rainey, an esteemed planner, was the managing director of Chiat Day. Kelly was the managing director of GGT.
Their agency was founded in 1993 and went on to create acclaimed work for Virgin Atlantic and Miller Genuine Draft. As the heads of Y&R's UK division, they oversaw the successful pitches for Marks & Spencer and Lloyds TSB.