The agency's brief is likely to develop the brand's drive to shake off its unsexy image and attract a younger audience to its services.
Alcone's work will aim to build on initiatives such as its spoof "Miss World" online pageant, which launched in November.
The appointment follows a six-way pitch at the beginning of the year that included incumbent agency Swordfish Marketing, Band & Brown and Dialogue.
Sandrine Schurer, consumer promotions and interactive manager at Teletext, said: "Our changing strategy will look more into partnerships and linking up with brands that share our values."
Schurer told P&I that these are likely to be a range of high-profile FMCG, entertainment and online brands.
Janet Hoy, director of Alcone, said: "Our key task is to educate the consumer about the availability of Teletext across a number of interactive TV platforms. Teletext is no longer only an analogue service."
Alcone said that it could not disclose details of forthcoming promotions because they are still at the initial planning stage.
Teletext now accounts for one in 11 of all holidays sold in the UK. The holiday brand is available on the web, digital satellite TV, digital cable TV, digital terrestrial TV and analogue TV.
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