The 76-year-old, who was paralysed from the waist down after a car accident in 1990, beat writers including Ian McEwan and Salman Rushdie to the honour.
The 60,000 prize, awarded every two years, will be presented to Achebe at a ceremony in Oxford on June 28.
Achebe was called "the father of modern African literature" by writer Nadine Gordimer, one of the judges, who added that he is "integral to world literature".
"What African literature set about to do was to broaden the conception of literature in the world - to include Africa, which wasn't there," Achebe told the BBC.
"In the stories we tell, it is intended to help us solve the problem of this failure that has overtaken the early sense of joy and happiness when Africans became independent, received their self-determination."
Another judge, academic Elaine Showalter, said Achebe had "inaugurated the modern African novel".
Chimamanda Ngozi Adichie, who recently won the Orange Prize for Fiction, said of Achebe: "He is a remarkable man. The writer and the man. He's what I think writers should be."
Others who have been nominated for the prize, which recognises a living writer for their body of work, included Doris Lessing, Philip Roth, Peter Carey and Margaret Atwood.
The recipient of the first honour - awarded in 2005 - was Albanian writer Ismail Kadare. (BBC)
