OMD landed the business after a pitch against MPG Media Contacts and Maxus in a process that was handled by the intermediary Tina Fegent.
Rapp is the incumbent on the charity's direct response media planning and buying business, and ZenithOptimedia handles the buying for above-the-line campaigns.
OMD's win follows the appointment in August of Inferno to the NSPCC's advertising account.
Earlier this year, the NSPCC hired the former Channel 4 head of strategic sales Mike Parker as the interim fundraising director to lead its consumer-facing marketing activity, replacing Paul Amadi. Parker left the charity last month.
In July, the NSPCC launched a hard-hitting online film to raise awareness of its helpline service, ChildLine, which urged children to speak out about physical abuse.Follow @nickbatten2