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.

They allegedly tailgated the vehicle before one of them climbed onto the bonnet of their van and broke into the truck in front of them.
Boxes of iPhones were then passed back through the van's roof.
The theft took place on the night of 24 July, on the A73 motorway near Horst.
Dutch news outlet ED said such gangs often modify their vehicles by putting an anti-slip mat on the bonnet.
The risky theft tactic was first seen in Germany in 2008, the outlet said. Belgium has witnessed similar incidents, almost all targeting smartphones. Sometimes, a grinding wheel is used to break into the truck.
Police spokesman Ed Kraszewski said Dutch police had been investigating truck thefts for some time, but doubted a theft like this could be pulled off.
"The truck was taking its freight from A to B and did not stop. Even so [the phones] were gone," he said. "So it must have happened that way. And now we finally have the evidence, with the van and the loot."
The men, aged from 33 to 43, were arrested on Saturday at a holiday park in Otterlo, in the central province of Gelderland.
Police found iPhones at the address, and the van they believe was used in the crime.
The men are set to appear before a judge on Tuesday.
British poet and journalist James Fenton has won the Pen Pinter Prize, which celebrates champions of free speech.
[NEXT_CONCEPT]
Five Romanian men have been arrested in the Netherlands on suspicion of stealing iPhones worth 500,000 euros ($590,000; £447,430) from a moving truck.