It happened in the early hours of Friday morning when Anis Amri was spotted acting suspiciously and asked for his identity papers.
He immediately opened fire, injuring one officer, and was killed in the shootout that followed.
An international manhunt had been underway for the 24-year-old Tunisian since Monday’s attack in Berlin which killed 12 people and injured dozens more.
Italian officials said there was no doubt the man shot dead was Amri, who reportedly travelled to Italy on the train from France.
Amri arrived in Italy via France - Took train to Turin, then went to Milan and Sesto San Giovanni https://t.co/uJM5LJZA0S— Ansa English News (@ansa_english) 23 dicembre 2016
Addressing a news conference, Italian Interior Minister Marco Minniti said:
“When it is possible to guarantee a level of security on the territory high enough for a person on the run
from several European countries to be identified and neutralised when he enters our country, then that shows that this system is able to work well.”
Minniti told reporters that Amri was stopped by two policemen at around 3 a.m. in front of the Sesto San Giovanni train station, north of Milan.
When he was asked for his identification documents, Amri pulled a gun and shot one of the two policemen, lightly wounding him in the shoulder. He in turn was then shot dead by the police.
“These two extraordinary, extremely young men, simply by doing their duty, have done an extraordinary service to our community,” Minniti said.
One of the two policemen had only just started service and was on his trial period.
ISIL has claimed responsibility for Monday’s attack, in which the hijacked truck mowed through a crowd of people and bulldozed wooden huts selling Christmas gifts and snacks beside a famous church in west Berlin.