Mr Mattarella, whose own brother was killed by the Mafia, described organised crime as a "pervasive cancer" that trampled on people`s rights.
He also promised to tackle the economic crisis and work for electoral reform.
Mr Mattarella assumed office at a ceremony at the Quirinale Palace in Rome, the official presidential residency, in front of the prime minister, his cabinet and the opposition.
He succeeds Giorgio Napolitano, 89, who stood down from the presidency earlier this month citing "signs of fatigue".
Italy`s presidency is largely a ceremonial role but it includes the power to appoint a prime minister, a power frequently invoked in Italy, where politics is famously volatile.
Mr Napolitano named five prime ministers during his eight-and-a-half-years in office.
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