A Thai court has ordered the extradition of a man accused of the 2009 murder of a Victorian man, after the 38-year old dropped his appeal against being sent to Australia to face trial.

Thatiya Terdputham, 26, withdrew the appeal against extradition to Australia to face trial in the murder of Melbourne chef Luke Mitchell.

But the appeal of Terdputham's co-accused, 31-year-old Surad Seehaverachart, remains before the Thai court, a spokeswoman for the Australian Attorney-General's Department told AAP.

In Melbourne, Mr Mitchell's brother, Shane, said the family was "very pleased" to hear the news.

"We didn't even know that the case was happening. But the family's very pleased that it's finally progressing in a forward motion," Mr Mitchell told AAP.

"The fact that one of them at least is going to have their case heard here is somewhat satisfying for the family."

Thatiya and Surad along with an alleged third co-accused - who remains at large - face charges of bashing and stabbing Mr Mitchell to death after he tried to save another man being assaulted outside a nightclub in northern Melbourne in May 2009.

The alleged killers fled to Thailand soon after the stabbing.

Both men, who were students in Australia, have pleaded not guilty to the murder, saying they had fought in self defence and claimed the third man was responsible for the killing. The men claimed the killer was the son of a mafia figure.

In November 2011 the Bangkok Criminal Court determined that both Thatiya and Surad could be extradited to Australia.

However, Australia does not have an extradition treaty with Thailand.

Thai prosecutors, acting on behalf of the Victorian Police and the attorney-general's department, had argued the case based on Thailand's extradition treaty with Britain, since Australia is a member of the British Commonwealth.

The Australian Attorney-General's Department spokeswoman said Australian and Thai authorities would now "work together to arrange for Mr Thatiya Terdputham to be surrendered to Australia".

She said the department would not comment on when the extradition may take place.

"It is long-standing government practice not to comment on operational matters, such as the timing or logistics of extraditions."

A Thai human rights organisation had earlier appealed to the Thai Foreign Ministry to intervene in the case and prevent any extradition arguing it would represent a breach of the men's "rights" and would also be "unsafe".