Armed Forces Minister Adam Ingram has given the go-ahead for investigator Frank Swann to enter the Deepcut Barracks.
Police are also looking into the deaths of the four, who all died from gunshot wounds.
The families, who are employing Mr Swann, have refused to accept the army's claim the soldiers committed suicide.
They have welcomed the move - announced by the Ministry of Defence (MoD) - as a major breakthrough and want a public inquiry after the police investigations are finished.
Mr Swann is to meet with army officers at the barracks on Monday to discuss how the forensic examinations will be carried out.
Speaking on BBC Radio 4's Today programme, he said: "Each has to be treated as an individual case, but there's a high probability that we will be able to establish (whether it suicide) in certainly three of them and maybe four."
Geoff Gray, 17, from Hackney, east London, died from two gunshot head wounds in September 2001.
Four deaths
Private Cheryl James, 18, from
Llangollen, north Wales, died Nov 1995
Private Sean Benton, 20, from West Sussex, died June 1995
Geoff Gray, 17, from Hackney, died Sept 2001
Private James Collinson, 17, from Perth, Scotland, died March 2002
His father Geoff, 38, said: "I think it's brilliant news. The more investigators who can look at this, the better. It's a huge step, whatever happens as a result."
Mr Swann added: "I think it is a major development in the sense that the families, their supporters and the media have been quite vociferous and I think it has made the MOD consider their position.
"I think it is a step in the right direction - and hopefully one towards more openness."
The army has been under pressure after it emerged that vital evidence such as paperwork and the soldiers' clothing were lost or destroyed.
In a letter to the families and their supporters, Mr Swann said: "My task is to apply strict scientific protocols and methodology, with the overriding factor of establishing whether the "Deepcut Four" self inflicted their wounds or whether they were killed by other person(s).
"It is not for me or my team to establish whether the deaths were murder, manslaughter, unlawful killing, accident or suicide.
"That is a matter for the police and Crown Prosecution Service if our scientific forensic team finds such evidence of criminal activity or otherwise.
"However, I must repeat that I have a reputation for telling it as it is, or was. Nothing or no-one will cause me to deviate from that path."