Eliot, whose seminal poem The Waste Land was published in 1922, came just ahead of Renaissance poet John Donne in the BBC poll.
Rastafarian poet Benjamin Zephaniah came third.
Thomas Stearns Eliot was born in St Louis, Missouri, in 1888.
He studied at Harvard and went on to teach at Oxford, making England his home.
The Waste Land is widely considered one of the most important poems of the 20th century.
His other works include Old Possum's Book of Practical Cats, produced in 1939 on the the eve of war, which was the inspiration for the musical Cats.
Eliot received the Nobel Prize for Literature in 1948 for his "outstanding, pioneer contribution to present-day poetry".
Donne, a contemporary of Shakespeare, was one of the leading metaphysical poets of the Renaissance.
Zephaniah, 51, was born in Birmingham. He left school aged 13 when he was still unable to read or write.
In 2003 he famously refused an OBE for his contribution to literature, commenting: "Me? I thought, OBE me? Up yours, I thought."
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