The judges praised Crossan's "exquisite writing style, thrilling plot, and masterful handling of teen issues".
As well as its unusual subject matter, One, published by Bloomsbury Books, is written in free verse.
Crossan received her Â£2,000 prize at Hay Festival from author and former children's laureate Malorie Blackman.
She beat competition from nine other authors - including Frances Hardinge's Costa Book of the Year, The Lie Tree - to win the YA Book Prize, judged by eight industry figures and four sixth form students.
One's main characters are 16-year-old Grace and Tippi whose upper bodies are separate but are joined at the hip and share one pair of legs.
Chair of judges Charlotte Eyre, children's editor for The Bookseller, said: "This blank verse novel is a remarkable achievement, being both beautifully written and gripping, and Sarah Crossan is one of the finest authors writing YA today."
Peter Florence, judge and director of Hay Festival, said: "It was an exhilarating shortlist and I'm thrilled by the winner. We've got a book that breaks every rule and would enthral any reader; a book that gives you the gift of reading in a new way and loving every page."
Originally from Dublin, Crossan grew up in Ireland and England then lived in New York for seven years. She worked as an English teacher for several years but gave that up to write full time.  Her other books include Breathe, Resist, The Weight of Water and Apple and Rain.
The YA Book Prize, now in its second year, is the only prize to specifically focus on fiction for young adults by authors based in the UK and Ireland.
At Thursday's ceremony, author Melvin Burgess also received a special achievement award to mark the 20th anniversary of his YA novel Junk.
The 10 books in contention for this year's YA Book Prize were:
Sarah Crossan's novel One, which tells the story of conjoined twins, has won The Bookseller's 2016 prize for young adult fiction.