The pair handed themselves into police after a Snaphcat image of the pair was posted online by The Border Mail.

Police said they had also received information from members of the public.

The 17-year-olds attended the Albury police station and told officers they were the people pictured in the photograph, which had the caption “taking a piss on monument”.

The incident is alleged to have occurred about 3am last Thursday.

Police are continuing to investigate the matter.

Albury RSL sub-branch president Graham Docksey said it was positive they had handed themselves in.

“From an RSL point of view, I’d like to see them do some research on two soldiers and then present it to one of my sub-branch meetings,” he said.

“I think that would develop a bit more of a social conscience in relation to respect for veterans, who have provided them a country that is democratic and free for them to express their own thoughts.

“This has only happened within a few weeks of Remembrance Day, when we’re forced to remember the country and the veterans who have sacrificed themselves for the county.”

Security cameras were installed at the site following previous acts of vandalism. 

Police said the teenagers would not be named due to their age. 

Members of the public had expressed outrage after the incident, with many lamenting the lack of respect they had shown. 

Mr Docksey said he wanted to offer the pair the chance to attend an RSL meeting. 

"That's purely between the parents and any court action that's likely to take place,” he said. 

“I want them to understand their actions and the consequences thereof.”

Mr Docksey said the teenagers had shown “great personal strength and courage to come forward". 

“I commend them for that," he said.  ​

Vice president Mark Dando agreed and said he wanted the pair to spend time in the military.