The agency won the business after a pitch against the ten-year incumbent, Delaney Lund Knox Warren & Partners, Publicis and Young & Rubicam.
Ogilvy's Copenhagen office led the pitch, with planning being run out of the London office.
Triumph had been expected to appoint two separate networks to handle the business for northern Europe and southern Europe respectively. However, O&M will work across both regions, with work running in a total of 12 countries across Europe.
Media is expected to stay with BJK&E Media.
Last year, DLKW created a campaign starring Trina, a virtual Lambada dancer in a supersoft bra with a 32 C bust, who danced to the 50s hit Vaba Ba Boom. The model and ex-presenter Kelly Brook was the voluptuous face of the Flaunt bra brand in a campaign launched in October 1998.
The Triumph portfolio includes the Triumph bra and lingerie range, the Valisere lingerie range, Sloggi underwear for women and Hom men's clothing.
No-one from either O&M or Triumph was available for comment as Campaign went to press.