The contracts, which were signed late on Wednesday afternoon, see Kelly and Campbell take a significant share in the agency.
WPP has bought Chime's 51% stake in the agency to facilitate the deal and to allow further investment in the United micro-network's ailing London Office.
Kelly and Campbell will fill the gaps left by Nick Howarth, the former chief executive, and the ex-creative director, Jonathan Burley, who quit the agency last year.
Kelly and Campbell were founding partners of Rainey Kelly Campbell Roalfe. They sold the agency to WPP in 1999, in a deal which saw it take on the Y&R name. In their new roles they will report to United's global and European chief executives, Andy Berlin and Amanda Walsh respectively.
Steve Henry, the chairman and co-founder of the agency, retains his senior network role, working with Walsh and United's chief strategic officer, Charlie Robertson. No redundancies are planned as part of the move.
In a hastily prepared statement, Berlin said: "Jim and Robert are perfect for United. These guys are proven entrepreneurs and have defined important moments in advertising. It's a very good match."
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