The bodies of 59 men, 8 women and four children are thought to have been dead for one-and-a-half to two days.
Police said the victims appeared to be migrants from Syria and probably died after suffocating in the vehicle.
Three people, thought to be Bulgarian, have been detained in Hungary. They are believed to have driven the lorry.
Police sent to investigate the dumped lorry on the A4 road towards Vienna discovered the decomposing bodies on Thursday morning.
The vehicle was towed to a customs building with refrigeration facilities in Nickelsdorf where forensic teams worked through the night to examine the bodies.
The vehicle bears the logo of a Slovakian poultry company, Hyza, which said it no longer owned the vehicle – but the buyers had not removed the branding.
The Hungarian prime minister’s chief of staff, Janos Lazar, said on Friday that the lorry was registered to a Romanian citizen in Kecskemet, a city in central Hungary.
Hans Peter Doskozil, police chief in the Burgenland province where the lorry was found, said it was a refrigerated vehicle – not the typical choice for people smugglers, he added.
The lorry, which has Hungarian number plates, is understood to have left Budapest on Wednesday morning.