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.

The 19-year-old was held in Barking on suspicion of being concerned in the commission, preparation or instigation of acts of terrorism.
Police said six other suspects remain in custody and searches are ongoing.
Eight people were killed when three men drove at pedestrians on the bridge and stabbed people in Borough Market.
The man arrested on Sunday is being held at a police station in south London.
The six men still in custody, all aged between 27 and 30, were also arrested in east London - four in Ilford, one in Newham and one in Barking.
Thirteen people arrested as part of the investigation have been released without charge, while a 33-year-old man held in Ilford on 8 June has been bailed.
Over the weekend, police released images of fake explosive belts worn by the three attackers, named as Khuram Butt, Rachid Redouane and Youssef Zaghba.
Borough Market is hoping to re-open "later this week", managing director Darren Henaghan has said.
Traders were officially given access to the market on Monday - for the first time since the terror attack - to allow them to start clearing up and prepare to resume business.
On Saturday night, bars and restaurants across the capital donated money to a British Red Cross UK fund for victims of terror attacks and their families, as Londoners were encouraged to show "unity and resilience" a week after the attack.
The fund has raised more than Â£700,000 since it started on 4 June.
And on Sunday, Southwark Cathedral - which had been cordoned off in the days after the attack - re-opened its doors for the first time.
David Harsent has won the TS Eliot Prize for poetry at the fifth attempt.
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Another man has been arrested in connection with the 3 June terror attack on London Bridge, bringing the total number of arrests to 21.