Accepting his award, Reid said: "I am absolutely delighted and bewildered to be the recipient of this important literary prize.
"The book itself was difficult to write, but it has had a very happy time since it fell into the hands of my publisher."
COSTA BOOK FINALISTS
Colm Toibin - Brooklyn (novel)
Christopher Reid - A Scattering (poetry)
Raphael Selbourne - Beauty (first novel)
Graham Farmelo - The Strangest Man (biography)
Patrick Ness - The Ask and the Answer (children)
Reid thanked the judges for their "generosity and kindness".
It is only the sixth time a poetry book has won the award, with Ted Hughes and Seamus Heaney each winning twice.
Speaking to the BBC, Reid said he was "obviously delighted" to be in the same company.
A Scattering includes four poetic sequences, the first written during his wife's final illness and the remaining three at intervals following her death.
Reid said: "She was given a very short time to live by her doctors and therefore I was given a very short time to say something on the subject, which I tried to do in the poems at the beginning of the book.
"I wanted to tell her somehow through these poems why I would be missing her when she went, and luckily I was able to finish that sequence before she died."
Introducing the finalists, author Josephine Hart, who was chair of the judges, said the panel was "full of admiration" for all of the books.
But she added that the final decision was arrived at by a "substantial majority" and described the collection as a "master work".
Hart continued: "We feel that what Christopher Reid did was to take a personal tragedy and to make the emotion and the situation universal.
Christopher Reid won the Costa Book Prize
"It is bizarrely life-enhancing because it speaks of the triumph of love before and after death."
She added: "It's packed with lines that are unforgettable... We all felt that this is a book we would wish everyone to read from late adolescence, 14 to 15 years old onwards.
"We regard this work as austere and beautiful and moving."
Reid beat bookmaker's favourite Colm Toibin, who won the novel award earlier this month with Brooklyn, to take the prize.
The award's categories are split into novel, first novel, poetry, biography and children's book, with each individual winner pocketing £5,000.
Other contenders had included Raphael Selbourne, who won the first novel award for Beauty, the story of a young Bangladeshi woman on the run from an abusive marriage.
Graham Farmelo was in the running for The Strangest Man, the book, which landed the biography title, about the life of physicist Paul Dirac.
Patrick Ness was up for the prize after winning the children's book award for The Ask and the Answer which the judges acclaimed as "a major achievement in the making".
A Scattering has also been nominated for the UK's two other top poetry awards - the Forward Poetry Prize and the TS Eliot Prize for Poetry.
Originally established in 1971 by Whitbread, Costa took over the sponsorship of the prize in 2006.
Since the introduction of the Book of the Year award in 1985, it has been won nine times by a novel, four times by a first novel, five times by a biography, six times by a poetry collection and once by a children's book.
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