Italy's interior minister has said the man killed was without doubt the Berlin lorry attack suspect.
Amri was fatally shot after firing at police who had stopped his car for a routine identity check around 3am local time (2am GMT), minister Marco Minniti told a press conference in Rome.
A manhunt had been on for Anis Amri after German authorities released a 23-year-old Pakistani asylum seeker, who had been detained in the hours following the terrorist attack.
Dozens of people were also injured when a truck was driven into the market and the 12 dead included a Polish man who had been driving the truck before it was hijacked.
German authorities said Amri's fingerprints were found in the cab of the truck, leading them to believe there was a "high probability" he was the man who drove the lorry into the crowded market in west Berlin.
Amri was put under court surveillance by German authorities for more than six months this year but agencies stopped watching him in September. Orders had been sent out for him to be deported, though he could not be deported without a Tunisian passport. His passport reportedly arrived this week, after he had carried out the attack.
Echoes of earlier attacks
Monday's attack had overtones of a similar terrorist attack on Nice, France, in July.
A 19-tonne cargo truck that was deliberately driven into crowds on one of the city's main promenades during Bastille Day celebrations, killing 84 and injuring at least 100 more. A Tunisian resident of France, Mohamed Lahouaiej-Bouhlel, was the driver.
Tunisia has been the sole success story of the Arab Spring uprisings that swept through the Middle East in early 2011. Last year, the country's National Dialogue Quartet, which spent months hashing out a secular, almost universally applauded new constitution after dictator Zine El Abidine Ben Ali was overthrown, won the 2015 Nobel Peace Prize.
However, Tunisia has struggled with pockets of strong Islamist support that has made it the top source of Isis recruits and spawned the 2015 Sousse beach resort shooting attack, which killed 38 people (30 of whom were Britons).