Eamonn Harrison, from County Down, Northern Ireland, is wanted for his alleged role in transporting the trailer in which the bodies of eight women and 31 men were found on an industrial park in Essex last year.
The court was told Mr Harrison is accused of 41 offences – 39 counts of manslaughter, which carries a maximum sentence of life imprisonment, one human trafficking offence, and one count of assisting unlawful immigration.
He is alleged to have driven the container to the port of Zeebrugge in Belgium and later signed the shipping notice for it.
Justice Donald Binchy said he approved Mr Harrison’s extradition after hearing comprehensive arguments from both sides.
His full judgment on the ruling will be made public on Monday next week.
Justice Binchy added that it would not be helpful for him to try to summarise his decision to the court.
Mr Harrison’s defence counsel, Tony McGillicuddy, said he would read the judgment next week and decide whether to appeal the decision.
The extradition order has been deferred to give the defence team time to consider the judgment, which runs to about 50 pages long, Justice Binchy said.
“It would not be fair to put such pressure if the respondent chooses to appeal,” he added.
Mr Harrison has been remanded into custody and will appear again at Dublin’s High Court on 4 February.
“The whole nation and indeed the world has been shocked by this tragedy, and the cruelty of the fate that has been suffered by innocent people who were hoping for a better life in this country,” Mr Johnson wrote in a book of condolences for the victims last year.
“We mourn those who have lost their lives. Our thoughts are with their families far away.”
In November, Maurice Robinson, a lorry driver who was allegedly part of a global smuggling ring, pleaded guilty to plotting to assist illegal immigration over the incident.
Additional reporting by PA