The agency defeated Agency Republic, Arc, Wunderman, BA's UK direct agency of 20 years, Tullo Marshall Warren and one other agency. Lida, which handles BA's holidays business in the UK, was not involved in the process.
The three-year contract covers all direct and online communications across the Asia-Pacific region.
The online task includes digital strategy and mobile marketing, digital media planning and buying, which will be handled by Neo@Ogilvy, and search marketing.
Annette King, OgilvyOne London's deputy managing director, said: "Creatively and strategically, it will present us with some exciting challenges. Asia and the Pacific is a rapidly developing market, and you have a uniquely complex set of brand communications issues to solve."
Daniel Lloyd, BA's marketing communications manager for Asia and the Pacific, said: "OgilvyOne demonstrated a real passion for the British Airways brand and presented us with excellent strategic and creative ideas."