The driver of the lorry, a 25-year-old man who was arrested was charged with 39 offences of manslaughter, money laundering, human trafficking.
Police in the UK said today that bodies found in a refrigerated truck last month in Essex were from Vietnam.
The Essex police worked with Vietnamese police officials to verify the identity of 39 people discovered at Grays in Essex on October 23. The lorry trailer was travelling from Zeebrugge in Belgium to Grays, Essex.
The victims included eight women and 31 men.
The Vietnamese embassy in London said it was "in deep sorrow, we would like to convey our profound condolences and sympathy to the bereaved families."
The Vietnamese embassy said it would "provide consular protection and support for the bereaved families in order to bring their loved ones home at the earliest time".
The driver of the lorry, a 25-year-old man who was arrested was charged with 39 offences of manslaughter, money laundering, human trafficking and conspiracy to assist unlawful immigration.
The Essex police also worked with National Crime Agency and European law enforcement officials to identify the bodies in the lorry.
The police had earlier urged Ronan Hughes, 40 and his brother Christopher Hughes, 34 from Northern Ireland on suspicion of manslaughter and human trafficking in connection with the deaths of 39 people.
The police later said Eamon Harrison, 23, from Northern Ireland, was accused of manslaughter and human trafficking and immigration offences. Harrison was remanded in custody until November 11.
The investigation is also underway in Vietnam after police said had held eleven people and summoned others for questioning.
Reports said most of the victims were from central Vietnam who travelled abroad illegally to Europe via Russia.
Vietnam said it "strongly condemns human trafficking and considers it a serious crime", while calling upon other countries in the region and around the world to step up cooperation in combating human trafficking.
British officials had earlier claimed that the migrants may have been from China linking it to another case in 2000 in which 8 Chinese were found dead in a tomato truck at the port of Dover, however, today officials confirmed all the migrants were from in fact from Vietnam.