The £5,000 prize for Birthday Letters follows the Forward Poetry Prize, which Mr Hughes won last year shortly before he died of cancer, aged 68.
TS Eliot's widow, Valerie, presented the prize to Mr Hughes's daughter, Frieda, at a British Library ceremony on Monday night.
Judges for the Poetry Book Society said: "It suggests that the search for a poet to take on his mantle may be even more difficult than early signs indicated."
The Birthday Letters was Mr Hughes's first break with a self-imposed silence on his grief over the break-up of his marriage to Sylvia Plath and her suicide.
The verses are also in the running to win the Whitbread poetry prize, to be announced on Wednesday.
Sarah Corbett, Fred D'Aguiar, David Harsent, Jackie Kay, Glyn Maxwell, Paul Muldoon, Ruth Padel, Jo Shapcott and Ken Smith are also on the shortlist.
Judges' chairman Bernard O'Donoghue said: "In any other year, any of these books would have been a fine winner of the prize, but this year the towering presence of Hughes's accomplished, powerful and utterly cohesive collection could not be overlooked.
"It is a truly great book."
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And the nominations are ...
(06 Nov 98 | Entertainment)
Quiet man of intense verse
(29 Oct 98 | UK)
Extracts from Hughes' Birthday Letters
(29 Oct 98 | Entertainment)
Ted Hughes Pages
International Poetry Hall of Fame
TS Eliot - Poetry and Prose
TS Eliot Hypertext Project
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