Private Cheryl James, 18, was found dead from a single gunshot wound in November 1995. An inquest recorded an open verdict.
She was one of four soldiers who died from gunshot wounds at the Surrey barracks between 1995 and 2002 amid claims of bullying and abuse.
The others were Privates JamesCollinson, 17, from Perth; Sean Benton, 20, from Hastings in East Sussex; and Geoff Gray, 17, from Seaham in County Durham.
Mr Justice Mitting and Judge Peter Thornton QC said there was "an insufficiency of inquiry" at the 1995 inquest and quashed its open verdict.
Judge Thornton said "the discovery of new facts or evidence" made "a fresh investigation including a fresh inquest necessary or desirable in the interests of justice".
Pte Collinson's mother, Yvonne, believes his death was a "prank gone wrong" and has called for a public inquiry. Appeals for a fresh inquest were rejected in 2012.
Pte James was undergoing initial training at Deepcut when she was found dead with a bullet wound between her right eye and the bridge of her nose.
Her parents, Des and Doreen James, applied through human rights campaign group Liberty for a new inquest after the Human Rights Act was used to secure access to documents held about the teenager's death.
Mr and Mrs James said they were delighted to have a fresh inquest but that "a meaningful inquiry into Cheryl's death is almost 20 years late".
They said: "When young people die in violent circumstances, a rigorous and transparent investigation should be automatic.
"Something went dreadfully wrong at Deepcut, yet until now no-one has bothered to look at how and why our daughter died.
"We can only hope that Cheryl's legacy helps change the current ineffective and discredited military justice system."
Liberty solicitor Emma Norton said: "Cheryl's family refused to let her death be swept under the carpet but they've had to fight at every stage for answers in the face of a state that thought it could ignore the basic human rights of its troops.
"Cheryl was preparing for a life of service and deserved so much better - her family can now hope to finally get some answers."
The new investigation is to be carried out by the current senior coroner for the Surrey area, who did not conduct the original inquest, or by a coroner to be agreed by the senior coroner, the Chief Coroner and Judge Thornton.
Pte James was a recruit with the Royal Logistical Corps when she died. She had been posted to a gate alone, in battle dress and armed with an SA80 rifle.