He was presented with a prize of Â£15,000 for his story Briar Road at an event at the BBC's Radio Theatre in London.
The Curious Incident of the Dog in the Night-Time author Haddon was the runner up for his story Bunny.
Brighton-based Buckley said the award was "a huge and delightful surprise".
He is the author of nine novels, most recently The River is the River.
Chairman of Judges Allan Little said: "Jonathan Buckley's Briar Road is a quiet, intriguing mystery and focuses on a single moment in the life of one family who have turned to a spiritualist after their teenage daughter has disappeared.
He described Buckley's writing as "understated, stark and plain", adding: "The intrigue builds as key details are revealed slowly, hinted at and suggested rather than spelled out."
The winner was announced on BBC Radio 4's Front Row programme.
Haddon's story Bunny tells of a morbidly obese housebound man who finds love in an old school friend.
Little called it "compassionate, touching and darkly funny".
Mantel's work, The Assassination of Margaret Thatcher, is set four years after Margaret Thatcher became Prime Minister in 1979 and imagines an IRA attempt on her life.
The two other shortlisted authors were Frances Leviston and Jeremy Page.
Gwyneth Williams, controller of BBC Radio 4, said: "I am thrilled to celebrate 10 years of our BBC National Short Story Award with such exceptional stories and gifted writers.
"Radio 4 is proud to broadcast more short stories than anyone, anywhere in the world.   Writers and original writing lie at our very heart."

Oduwa, 19, and Ball, 20, represent manager Mark Warburton's eighth and ninth signings of the summer window.
Both Players are a product of the Tottenham youth system.
Ball spent the second half of last season on loan at Cambridge United, making 11 appearances, whilst Oduwa also appeared 11 times for Luton town.
Ball has represented England at Under-19 and Under-20 level, having previously represented Northern Ireland at younger age groups.
Oduwa has also played for England at youth level, representing his country at the Under-18 level.
Warburton will have both players available this Sunday as Rangers continue their Championship campaign away to Alloa.
Former Rough Guides editor Jonathan Buckley has beaten Hilary Mantel and Mark Haddon to win the 10th annual BBC National Short Story Award.
[NEXT_CONCEPT]
Rangers have signed winger Nathan Oduwa and defensive-midfielder Dominic Ball on a season-long loan from Tottenham Hotspur.