The agency won the business after a four-way pitch against MediaCom, Media-Vest Manchester and Manning Gottlieb OMD.
Telegraph Group's decision to appoint a media buying agency comes amid increased speculation that it is gearing up for the launch of a tabloid edition of The Daily Telegraph to rival The Times and The Independent.
However, uncertainty over its ownership may delay this.
Telegraph Group is Universal's second major new-business win in a fortnight, after its capture of the £10 million RHM media account.
It won the newspaper's buying account following MindShare's decision to resign it last November after the publisher moved the media planning business into Naked Inside, a joint venture between Naked Communications and The Telegraph's creative agency, Clemmow Hornby Inge.
Universal's pitch team was led by Andy Jones, its recently appointed joint managing director. Posterscope will handle outdoor buying.
Mark Dixon, the marketing director of Telegraph Group, said Universal had won the business "after a highly competitive pitch and some excellent presentations".
Jones said: "The opportunity to work with such a prestigious client is a huge compliment to Universal McCann."