In a statement on Thursday, Essex Police said the relatives of the victims have been informed, reports Efe news.
On October 23, 31 men and eight women were found inside the refrigerated chamber of the vehicle in an industrial park in the town of Grays, in southeast England.
"This is an important step in the investigation and enables us to work with our Vietnamese Police colleagues to support the families of those victims," a senior officer in charge of the enquiry, Assistant Chief Constable Tim Smith, said in a statement.
"It is only right that we provide an opportunity for family members to take in the news confirming the death of their loved ones before releasing any further information.
"Our thoughts remain with the families and friends of those whose tragic journey ended on our shores," he added.
Authorities in Vietnam confirmed that the victims were Vietnamese nationals and specified the provinces they had travelled from as Hai Phong, Hai Duong, Nghe An, Ha Tinh, Quang Binh, Thua Thien and Hue.
The Vietnamese Ministry of Public Security added that the victims have been identified with the help of the British Police.
The announcement was made after a Vietnamese delegation travelked to the UK on November 2 to work on the identification of victims.
So far, 35 families from the provinces of Nghe An, Ha Tinh and Quang Binh have reported the disappearance of relatives.
Some parents have already received official notification that their children were among the 39 dead in the Essex truck.
To An Xo, a spokesman for the Ministry of Public Security, said that the date and manner in which the bodies will be repatriated will depend on the British authorities and the families.
Vietnamese police have detained 11 people in the Ha Tinh and Nghe An provinces in recent days allegedly linked to the trafficking of the victims from Vietnam to Europe.
It is thought some migrants had paid up to $40,000 to travel to the UK.
The truck in which the deceased were found had travelled from the port of Purfleet in east London, where it had arrived from the port-city of Zeebrugge in Belgium.
The cabin driver, a 25-year-old Norwegian named Maurice Robinson, appeared before a British court charged with 39 counts of manslaughter and other crimes.
Two others have also appeared in a Dublin court for their alleged relationship to the crime.
( With inputs from IANS )