The memorial, which stands at 4ft high, was carved by stonemasons at Salisbury Cathedral.
It will sit on a lawn within the visitors' area of the category C prison in Wiltshire.
During a ceremony held at the prison on Tuesday, the Dean of Salisbury, the Very Reverend Nicholas Papadopulos, dedicated the memorial.
He formerly worked as a barrister specialising in criminal law before joining the church.
"It is very easy to regard prisoners as 'out of sight and out of mind', and to leave the job of rehabilitation to others," he said.
"But we all must take responsibility for the society in which we live, and strive to make it better.
"I am incredibly proud of what has been achieved by the prisoners and our masons working together.
"We must cherish the hard-won rights and freedoms we enjoy today, inside and outside the prison system, whether working together to create something as meaningful as this memorial, or simply taking time to pause and reflect on the sacrifice of others."
The badges of the Army, Navy and Royal Air Force have been carved on the monument - with the words land, sea and air inscribed beneath.
A gun with a helmet is on the fourth side of the structure, under the quotation: "Now listen, For a moment, The world is silent, Peace be with you".
All prisoners will pass the war memorial as part of their daily routine.
Prisons Minister Rory Stewart said: "This memorial is a moving tribute to the fallen soldiers who lost their lives bravely serving our country.
"I am grateful to Salisbury Cathedral for giving offenders from HMP Erlestoke the chance to participate in this hugely worthwhile project.
"Such opportunities provide a true sense of purpose - helping to support rehabilitation and allowing them to give back to society."
The memorial is part of a wider First World War centenary initiative within the prison, which was conceived by the prisoners themselves.
Prisoners also worked to create a magazine of poetry and writings about the First World War. One drew more than 100 pencil portraits of every Victoria Cross winner during the conflict.
Tim Knight, governor of the prison, said: "There's no doubt that there are challenges managing a prison like this, but that shouldn't overshadow the remarkable work being done by our dedicated and passionate team.
"We are committed to working with partner agencies like Salisbury Cathedral to provide intervention programmes, and skill and vocational based training and education to make a difference.
"We hope that by offering prisoners opportunities to participate in projects like this we can assist in their rehabilitation. None of this is a simple fix, but our long-term goal."
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