The agency triumphed in a three-way pitch against Lowe London and Publicis.
RKCR/Y&R will produce a print, ambient media, radio and point-of-sale campaign aimed at 17- to 20-year-old first-time applicants.
The ads will break in the new year, and be based on a strategy developed by the Home Office, COI and Naked Communications, which was appointed to the account earlier in the year.
From the end of this year, first-time applicants will be required to take part in a face-to-face interview with a passport officer at one of 69 passport offices in the UK.
In September, new passports were introduced with a digital chip that can carry biometric data, including precise facial measurements. From 2008, the chips may include iris scans and fingerprints.
The RKCR/Y&R chief executive, James Murphy, said: "When issues such as passport fraud are so high on the public agenda, it's very exciting to get a brief in that area."
Government figures put the total cost of switching from standard to biometric passports at around £60 million.
The changes to the UK passport rules are part of government measures to clamp down on identity fraud and respond to fears of terrorism.
According to the Identity and Passport Service, 74 per cent of fraudulent passport applications are made by first-time applicants.