Hamilton and Daniel Coyle wrote the account, which made sensational accusations against Lance Armstrong that were subsequently supported by the US Anti-Doping Agency's mammoth dossier of evidence.
It is the third time a cycling book as won the award after Paul Kimmage's Rough Ride in 1989 and Armstrong's own It's Not About The Bike in 2000.
Hamilton said: "This is really special. I'm really proud of writing this book but not what's in there. But it's the truth and the truth needed to be told."
Hamilton helped Armstrong to three of his seven (now annulled) Tour de France victories as a team-mate at US Postal.
He was caught in a complex doping case that eventually saw him stripped of his time trial gold medal from the Athens Olympics in 2004.
After initially protesting his innocence, Hamilton owned up and became one of the key figures in exposing Armstrong.
Also shortlisted for the award were Rick Broadbent's Inside the TT; Adharanand Finn's Running with the Kenyans; Simon Jordan's memoir Be Careful What You Wish For; Fibber in the Heat by Miles Jupp, A Life Without Limits – A World Champion's Journey, by Chrissie Wellington; and Shot and a Ghost: A Year in the Brutal World of Professional Squash by James Willstrop with Rod Gilmour.