The remains of Private James Collinson, 17, were exhumed from a cemetery in Perth and later reburied.
It is part of a fresh investigation by Surrey Police into the death of four young soldiers at the army base over the last seven years.
They all died from gunshot wounds.
A spokesman for the Collinson family said they had endured a "tense and difficult day".
The family were not present during the exhumation nor at the post-mortem examination.
Surrey Police said they were awaiting the pathologist's report and the result of any forensic tests.
Deepcut, the Royal Logistics Corps HQ, has been at the centre of allegations of bullying.
John Cooper, a barrister representing some of the families, spoke on behalf of the dead soldier's relatives.
He said: "It has been necessary that this step was taken in our inquiry to find out what happened."
The Army has said that Pte Collinson committed suicide after his body was found with a single gunshot wound to his head in March this year.
A coroner returned an open verdict on the death.
Private Collinson's father, Jim Collinson, told the BBC Scotland Frontline programme: "It has always been at the back of our minds - was there a proper post-mortem done on James?
"Did they look for every piece of evidence?
"And now that they're going ahead and exhuming him it's just one great relief, you know, at last we've got the opportunity now to look at every piece of evidence that could be there."
The exhumation comes amid growing concern about three other similar deaths at the camp over recent years, which were all reported as suicides.
Last September Geoff Gray from Seaham, County Durham, was found shot dead on guard duty at the Princess Royal Barracks.
Private Cheryl James, 18, from Llangollen, north Wales, was found in 1995 lying in woodland outside the base with a single bullet hole in her head.
In the same year 20-year-old Sean Benton from Hastings, Sussex, was found dead with five gunshot wounds.
In the BBC documentary this week Frank Swann, a leading ballistics and forensic expert, said it was "impossible" that Private Gray killed himself.
His father - also called Geoff - said Mr Swann's evidence strengthened his claim that his son had been murdered.