The agency won the account after a competitive pitch against Havas Worldwide London and JWT London.
A review of the business began in July and was conducted by The Observatory International and Claudia Falcone, the global brand director at Peroni.
Peroni works with The Bank on its global advertising account, which will be unaffected by the appointment. Arc and Holler will no longer work with the brand in the UK. Peroni spends £3 million on above-the-line advertising in the UK.
Arc was appointed to Peroni's direct marketing account in February, while Holler was awarded its digital business after a competitive pitch last month.
The Bank was behind Peroni's "primavera/estate" global campaign last year, which featured fashionable men and women in Italy during the summer months. The 60s-style ad used the recording artist Mario Biondi's version of the track My Girl.
The brand also released a six-minute film, Senza Tempo, or Timeless, in 2010. The film was set in Rome and narrated in Italian with English subtitles. It was directed by Gabriele Muccino, the man behind the films The Pursuit Of Happiness and Seven Pounds.
It told the love story of a heartbroken director and did not mention Peroni, opting instead to feature subtle camera shots of the brand.Follow @SaraKimberley