Established in honour of playwright Harold Pinter, it is given to a writer who casts an "unflinching, unswerving" gaze upon the world.
Organisers English Pen praised Fenton as "one of the finest poets of his generation".
He will receive his award at a ceremony on 6 October at the British Library.
The prize will be jointly awarded to an international writer who has faced persecution.
The second winner - who will be chosen jointly by Fenton and English Pen - will be announced at the October ceremony.
'Spoken truth to power'
Fenton, who held the chair of Oxford Professor of Poetry from 1994-1999, has written several collections of poetry and opera librettos.
As a former war correspondent, many of his poems deal with the experience of war and its impact.
One of Fenton's most acclaimed works, The Memory of War (1982), is a collection of poems that drew on his time as a reporter in Vietnam and Cambodia in the 1970s.
Antonia Fraser, Harold Pinter's widow, said Fenton was "a worthy winner" of the prize.
"James Fenton is a writer who Harold Pinter much admired for all his work, but particularly for his ability to write brilliant political poetry, she said.
"This is an art which was very important to Harold not only for the poetry but also as part of the essential process of speaking up fearlessly: Which is the basis on which the Pen Pinter Prize is founded."
Maureen Freely, president of English Pen, added: "Throughout his long and distinguished career, James Fenton has spoken truth to power - forcefully, fearlessly, and beautifully."
Fenton said he felt greatly honoured to be awarded the prize: "In particular, I am happy to be connected in this way with Harold Pinter, whose writings I have long admired."
Previous winners of the Pinter Prize include Tom Stoppard, Carol Ann Duffy, Hanif Kureishi and last year's winner, Salman Rushdie.
British poet and journalist James Fenton has won the Pen Pinter Prize, which celebrates champions of free speech.