Louise Waddington-Irvine, an account director at the agency, will field calls for the teetotal couple, who have made headlines over the naming of their daughter, Apple, and Paltrow's zest for alternative health remedies.
Record label EMI will continue to handle music press for Martin, whose band is currently working on a third album.
Former Sky TV senior publicist Waddington-Irvine said Monk's PR would be "just reactive" and the agency had been drafted in to cope with the "volume of calls about them as a couple".
Paltrow's relationship with Los Angeles-based entertainment PR firm PMK is unaffected by Monk's appointment and Coldplay continue to be managed by Estelle Wilkinson.
Martin, who has strong views on issues such as fair trade, was involved in a bust-up with a photographer in Australia last year. Police charges were later dropped.
Monk sealed a contract to handle PR for footballer Wayne Rooney four weeks ago.
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