Anis Hanachi was arrested Saturday night in Ferrara, Italy, after French authorities issued an international arrest warrant.
French investigators, who suspect Anis of complicity in his brother's attack, indicated that he had "fought, waged jihad in Syrian-Iraqi territory, with military experience," Lamberto Giannini, head of Italy's counterterrorism team, said at a press conference.
"A hypothesis that remains to be verified is that it was him who indoctrinated his brother Ahmed and caused his radicalisation," Giannini said.
He had lived for several years in Aprilia, south of Rome, where he married an Italian woman.
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He was not known to attend any mosque, but was known to the police for drug and alcohol problems.
The Islamic State group has claimed responsibility for the attack, but French investigators have yet found evidence linking it to the jihadist fighters.
The only trace of Anis in Italy, however, went back to 2014, when he arrived with other migrants on a boat and was sent back to Tunisia, which Italy now does with nearly all Tunisians who arrive on its coasts.
But analysis of his fingerprints, which had been taken when Anis arrived in Italy in 2014, confirmed his identity.
So far he has not been cooperative with the authorities, the Italian police said, and his extradition to France could happen in "a few days".
Several jihadists who have struck in Europe, including Anis Amri, who slammed a truck into a Berlin Christmas market in 2016, travelled through Italy.
But for now, "we have not established any common framework of conduct that could make us think that there could be something here in Italy constituting a (logistical) base for striking elsewhere," Giannini said.