A third migrant was seriously injured and taken to hospital, the police in the western province of Tyrol said, adding that the migrant's nationalities were not known.
Having been swept up in Europe's migration crisis last year, Austria led a coordinated effort with Balkan countries to shut down what was then the main route into the heart of Europe for hundreds of thousands of people, many of them fleeing war and poverty in the Middle East and elsewhere.
As the flow of people into Europe shifted this summer towards the sea route linking North Africa to Italy, Austria threatened to introduce border checks at the Brenner crossing, a vital transport link connecting Italy to northern Europe, if too many migrants headed its way.
But that influx did not materialise and Austria has praised Italy's work in keeping the number of migrants headed towards it at a low level.
The Austrian police said the migrants killed and injured on Saturday were likely headed for Germany, the country most migrants arriving in Europe have been trying to reach. The town at which the trucks were unloaded, Woergl, is roughly 15 km (24 miles) from Austria's border with Germany.
The train, which has no roof, is an alternative to driving trucks across the border. It also goes through the Brenner pass.
A police spokesman said the migrants were hiding under the trucks and would have had about 20 minutes to leave between when the trucks switched on their engines and started moving.
‘Since they stayed lying there we assume that because of the cold they may have lost consciousness or were perhaps already dead,’ he said, adding that the temperature in Woergl had been around -2 Celsius (28 Fahrenheit).
Immigration has become a sensitive issue in Austria, which is holding it presidential election on Sunday, in which Freedom Party candidate Norbert Hofer could become the first freely elected far-right head of state in Europe since World War Two.
