The prize was announced this morning at a gala dinner in London.
Catton, 22, receives a £50,000 prize for the award.
She is the second New Zealander to win the Booker. Keri Hulme won in 1985 for The Bone People.
Lloyd Jenkins was shortlisted for Mr Pip in 2007.
In accepting the award, Catton said her book was "a publisher's nightmare.''
She said she was very aware of the pressures on contemporary publishing to make money.
"It is no small thing that my primary publishers ... never once made those pressures known to me while I was writing this book,'' she said.
"I was free throughout to concern myself not of questions of value, but of worth.''
She was presented with the award, one of the world's highest literary prizes, by the Duchess of Cornwall.
Catton thanked her partner, poet Seve Toussaint and said his "kindness, patience and love'' was written on every page of her book.
At 28, she is the youngest person to win the booker.
The Luminaries is her second novel, and follows The Rehearsal, which was published in 2008.
In winning the Booker, the Auckland writer has become the youngest to take the prize.
That may have its downside. Catton has spoken of how making the Booker shortlist has cut her life in two: the "Eleanor'' public life, and the "Ellie'' private life.
"I can feel the public side of my life and the private side of my life sort of drifting away from one another.''
The Luminaries, an epic historical novel, is set in 1866 gold-rush Hokitika.
With its structure and narrative propelled by 12 men aligned to 12 signs of the zodiac, the 832-page murder-mystery has divided reviewers, electrifying many, baffling others.
The Man Booker judges described it as "a New Zealand Twin Peaks''.
As one observer has commented: "Her understanding of male characters, and prostitutes and smoking opium is amazing. It's as if she has lived a much more colourful, wild life than the young woman you read about or listen to on the radio.''
Not everyone has praised The Luminaries.
Critic Robert McCrum wrote in the Observer: "This sprawling mystery, a Victorian pastiche set in Victorian New Zealand, is replete with red herrings, astrological symbolism, and suspended revelations.
"A doorstop of a novel, by a New Zealander who appears to have swallowed a dictionary, it is by Trollope out of Wilkie Collins, possibly suckled by John Fowles.
"At more than 800 pages, it left this reader wishing that Catton had also paid homage to Robert Louis Stevenson whose best line, surely, is 'the only art is to omit'. On page 342, Catton supplies a story-so-far from the point of view of the protagonist Walter Moody. If you are unemployed, or marooned on a desert island, this timely round-up might give you the courage to investigate the next 500 pages.''
Jim Crace was seen as the narrow favourite to take the Booker with Harvest, with Catton put at second-equal with Colm Toibin's The Testament of Mary.
In her speech, Catton said she was influenced by the book The Gift by Lewis Hyde, which helped her understanding of the West Coast during the gold rush years.
"The region is rich in two very different minerals, gold, prized by Europeans for its value, and Greenstone or Pounamu, prized by Maori for its worth.
"Gold being pure currency, can only be bought and sold. Pounamu as a symbol of belonging and prestige, can only be given.
"An economy based on value, in Lewis Hydes conception, is not necessarily inferior to an economy based on worth, but the two must somehow be reconciled in the life of an artist who wishes to make a living by his or her gift, by his or her art.''
Catton said that intersection of economies on the West Coast had a national significance for New Zealand "speaking as it does to New Zealand's essentially bicultural heart''.
"I am very aware of the pressures on contemporary publishing to make money and to remain competitive in a competitive world, and I know that it is no small thing that my primary publishers, Granta, here in London, and Victoria University Press in New Zealand, never once made these pressures known to me while I was writing this book.
"I was free throughout to concern myself of questions not of value, but of worth.
"This is all the more incredible to me because The Luminaries is and was from the very beginning, a publisher's nightmare. The shape and form of the book made certain kinds of editorial suggestions not only mathematically impossible, but even more egregious, astrologically impossible.
"A very sensible email from one of my two editors ... might have even earned the very annoying and not at all sensible reply, 'well you would think that, being a Virgo'.
"I am very fortunate to have found a home at these publishing houses.''
Catton's New Zealand publisher, Fergus Barrowman of Victoria University Press, who attended the prize ceremony at Guildhall in London, said he was thrilled.
"We are delighted for Ellie and for the further international recognition the Man Booker Prize will bring The Luminaries,'' he said.
"It's a big ambitious book written by a fearlessly intelligent and talented writer. It's a novel for readers who love great storytelling and it's wonderful that the judges have chosen to recognise that with this illustrious prize.''
Victoria University Press said the book had been selling extremely well since and was now onto its fifth print run.
Friends and fans have rushed to congratulate Catton on her win, posting on her facebook page and Twitter.
On Twitter, #ManBookerPrize, Eleanor Catton and The Luminaries were the top three trending topics in New Zealand at 11am.
Writer Elizabeth Knox tweeted: "Just spoke to @FergusVUP on phone. There was trembling. Then cheers and tears.''
Novelist Rachel King, who had earlier tweeted that she was doing the school run in her best dress to mark the award ceremony, tweeted: "I think I'm crying. She looks so overwhelmed I want to hug her. Well done @EleanorCatton!``
Labour MP Jacinda Ardern said: "Huge congratulations to Eleanor Catton! Winner of Man Booker prize 28 yrs after Hulme won (the same year Eleanor was born) What an achievement''.
Findlay McDonald called Catton "The Lorde of literature!"
Nik Jarvie-Waldrom posted on Catton's facebook page: "Will toast to your success when I get home. For now, I shed tears at my work desk and prepare to monitor media reports about your incredible talent.''
Anne Kennedy wrote: "Congratulations, Ellie! Deafening roar out at MIT when you won. Then awestruck silence for your great speech. I knew you'd win!"
Jane Groufsky wrote that she had simultaneously burst into tears, jumped around her office, almost hyperventilated and ran to tell her co-workers, "who I don't know very well and it was somewhat awkward but I was just so damn excited.''
Catton wrote chapters of her award-winning book while Writer in Residence at the University of Canterbury (UC) in 2011.
The university's acting head of English, Christina Stachurski, said Catton received her Bachelor of Arts degree there after three years of study in 2005.
"We recognised Ellie as a writer of some exceptional talent and she was appointed Writer in Residence in 2011 when she wrote chapters of The Luminaries while based here on campus.
"Keri Hulme, was also UC's Writer in Residence here on campus when she won her prize for The Bone People, so that's a remarkable achievement for our Department and for UC.
"But today we are just so proud of Ellie. She worked in an office down the hallway here. She is a lovely person, unpretentious and fun to have around. Her father, Dr Phillip Catton, was a senior lecturer in philosophy here too,'' Stachurski said.
Catton's success should inspire aspiring writers of all ages to start writing the next great New Zealand novel, said National Librarian Bill Macnaught.
"I congratulate Eleanor Catton on becoming the youngest-ever Booker winner,'' said Mr Macnaught.
"And I note with pride that she credits her research on the Library's Papers Past website with providing insight into the historical period and places the novel is set in.
"The ethos of the National Library - whether its through our Services to Schools programmes or the hugely popular Papers Past site - is to give New Zealanders access to the knowledge we collect and turn it into value. And didn't she just.
"The National Library hopes Eleanor's terrific achievement will encourage other New Zealanders to find inspiration in the resources we provide.''
