The Havas-owned agency was shortlisted at the beginning of this month to compete in the final stage of the pitch, along with Publicis Groupe's ZenithOptimedia and WPP's Mediaedge:cia. At the time, incumbent Omnicom's PHD and Aegis agency Carat were ruled out from the original five-agency pitch list.
PHD had handled the BBC's media planning and buying account for 12 years.
The account covers all public-service elements of the corporation in the UK, including TV, radio, online, sports, factual and learning, and children. Media agencies had been invited to submit a tender via an ad in the Official Journal of the European Communities.
MPG will now be responsible for the delivery of media strategy and campaigns, but TV and radio work will be produced by the BBC's usual supplier Red Bee Media, formerly known as BBC Broadcast and which was its in-house production department until it was sold off in 2005.
Last October, the BBC appointed Rainey Kelly Ccampbell Roalfe/Y&R and reappointed Fallon to its ad agency roster.
The BBC adds to MPG's recent account wins, which include the £7m National Express media planning and buying brief and the £1m media account for kitchen and bathroom products manufacturer Salter.
The pitch is understood to have been led by MPG strategy director Marie Oldham, a former business development director at BBC Worldwide.