The lorry was discovered at the side of a road after it was abandoned by alleged people traffickers.
Those aboard had most likely died within minutes of being sealed inside the refrigerated lorry which crossed the border from Hungary into Austria.
Ten of those identified are believed to have originated from Iraq. Some additional persons are likely to be identified soon after information is provided by relatives.
Gerald Pangl, a spokesman for Austrian police, told journalists that it may be weeks or even months before the names of the deceased are known.
"One has to take into account that DNA samples have to be obtained from [relatives in] countries such as Afghanistan."
Much of the information for identification came from people who called a police hotline.
"Many of them said that they lost contact with their relatives on that day," Pangl said.