The posthumous award was for Birthday Letters, Hughes's book of poems about his relationship with Sylvia Plath. The book, which has already won the Forward Prize for poetry, could win another award today as it is on the best poetry collection shortlist for the Whitbread Book of the Year prize.
Last night, in a ceremony at the British Library, Mrs Valerie Eliot, T S Eliot's widow, presented a cheque for pounds 5,000 to Frieda Hughes, the daughter of Ted Hughes and Sylvia Plath, who received the award on behalf of her late father. Frieda Hughes will be publishing her own collection of poetry later this year, which will be dedicated "To Daddy With Love."
Bernard O'Donoghue a poet and Oxford University lecturer who chaired the judging panel, said: "In any other year, any of these books would have been a fine winner, but the towering presence of Hughes's accomplished, powerful and cohesive collection could not be overlooked. It is a truly great book."
Birthday Letters achieved extremely high sales for a poetry collection. According to sales data from Whitaker BookTrack it was the top selling hardback poetry book in high street shops in 1998. Figures published just before Christmas showed it had sold 48,453 copies, marginally ahead of the latest novel by Terry Pratchett.
Hughes's collection of 88 poems caused a literary sensation when it was published. It was the first time he had broken his silence about his stormy relationship with Plath and interest in the book grew even greater after his death.
The T S Eliot prize, which is in its sixth year is awarded by the Poetry Book Society.
The other poets shortlisted for this year's prize were: Sarah Corbett, Fred D'Aguiar, David Harsent, Jackie Kay, Glyn Maxwell, Paul Muldoon, Ruth Padel, Jo Shapcott and Ken Smith. The judges were Mr O'Donoghue and two other poets, Simon Armitage and Maura Dooley.
This year's prize had the bonus of a stay at Charingworth Manor Hotel, the setting for "Burnt Norton", one of Eliot's Four Quartets. A spokeswoman said a member of the Hughes family would be offered the weekend break.