Harsent won the prestigious £20,000 award for his eleventh collection Fire Songs. It was his fifth nomination, dating back to 1998, but he had not previously won.
Chair of the judges Helen Dunmore described Harsent as "a poet for dark and dangerous days".
She added: "Fire Songs plumbs language and emotion with technical brilliance and prophetic power."
This year's other nominees included former winners John Burnside and Michael Longley. The 10 shortlisted authors received £1,500 each.
To mark the 50th anniversary of Eliot's death on 4 January 2015, the prize money for the winner has been increased from £15,000 to £20,000.
Judges Dunmore, Sean Borodale and Fiona Sampson chose the shortlist from 113 books submitted by publishers.
The TS Eliot Prize 2014 shortlist:
Harsent's previous collections include 2005's Legion, which won the Forward Prize for best collection, and 2011's Night, which was shortlisted for the Costa, Forward and TS Eliot Prizes and won the Griffin International Poetry Prize.
He is currently professor of creative writing at the University of Roehampton and a fellow of the Royal Society of Literature.
Harsent was presented with his award at a ceremony at the Wallace Collection in London on Monday.
Previous TS Eliot Prize winners include Ted Hughes, George Szirtes, Carol Ann Duffy, Seamus Heaney, Derek Walcott, John Burnside, Sharon Olds and Sinead Morrissey.
The TS Eliot Prize was launched in 1993 to celebrate the Poetry Book Society's 40th birthday and to honour its founding poet. The prize money is donated by the TS Eliot estate.
David Harsent has won the TS Eliot Prize for poetry at the fifth attempt.