The man was out jogging at Val di Sole valley, near his village in Caldes, in the Trentino region, on Wednesday when he was fatally mauled.
Local media have identified the jogger as 26-year-old Andrea Papi.
His mauled body was found by a search team, hours after his girlfriend reported him missing.
Trentino region’s president, Maurizio Fugatti, said the bear that killed Papi would be identified and killed.
It’s believed there are around 100 bears now in the province.
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Some animal rights organisations have condemned the decision to identify and kill the bear.
Legambiente, an environmental association, said it’s the country’s first lethal attack in 150 years, adding there shouldn’t be a “witch hunt” against the animals in general.
In March, another man was attacked by a bear in the same region.
Val di Sole valley is a popular trail for hikers and tourists.