The minister told a press conference in Rome that Anis Amri had been fatally shot after firing at police.
The minister told a press conference in Rome that Anis Amri had been fatally shot after firing at two police officers who had stopped his car for a routine identity check around 3:00 am (0200 GMT).
Identity checks had established "without a shadow of doubt" that the dead man was Amri, the minister said.
He said that Amri had coolly pulled the weapon from a backpack and began shooting. One of the officers was hit in the shoulder during the exchanges, the minister said. The officer was in hospital, awaiting surgery but not in any danger.
Italy had Amri's fingerprints on file as a result of him having been in prison in Sicily between 2011 and 2015.
Thought to be around 24, he had been on the run since escaping after Monday's attack which left 12 people dead.
He had arrived in Italy from his native Tunisia during the Arab Spring in 2011.
Shortly after his arrival he was sentenced to a prison term for starting a fire in a refugee centre.
He was released in 2015 and made his way to Germany.
Media reports in Italy say he was on anti-terrorism police's radar as a potential Islamist radical during his time in prison but was not considered a high-priority subject for monitoring.