In his acceptance speech, Wright said: "Thanks very much. Just when I thought it was OK to relax, this happens."
After thanking friends, family, his fellow nominees and the Tate, he added: "I have nothing grand to say about that, just thank you, that's all I have to say."
Wright works predominantly with paint and gold leaf directly on walls to create intricate and graphic paintings.
He was shortlisted for the Turner Prize for his exhibitions at the 55th Carnegie International, Pittsburgh, and his exhibition at the Ingleby Gallery, Edinburgh, featuring his characteristic work.
Wright creates tailor-made artworks which are designed to fit each exhibition space. His contribution to this year's Turner Prize exhibition is an elaborate, gold-leaf fresco almost covering one wall of the gallery.
It took four weeks to make, which Wright described as an "intense process", and - like most of his work - is expected to be destroyed at the end of the exhibition.
He told the BBC the impermanence of his works was an important part of his art.
"I am interested in placing painting in the situation where it collides with the world; the fragility of that existence. Being here for a short period of time, I feel, heightens the experience of it being here."
He added: "Sometimes I feel a sense of loss because I can't repeat the work... but maybe that sense of loss is part of the point."
The Tate described the piece as the artist's "most complex and ambitious composition to date".
Poet Carol Ann Duffy announces the winner of the Turner Prize - Courtesy Channel 4 News
The award jury said they "admired the profound originality and beauty" of Wright's work.
The Turner Prize is awarded annually to a body of work by an artist under 50, and born, living or working in Britain.
Speaking at the ceremony, Tate director Sir Nicholas Serota said this year's Turner prize exhibition had been one of the most successful.
Poet Laureate Carol Ann Duffy, who presented the award to Wright, praised the shortlisted artists. She said: "This years shortlist shows we have some of the most inventive artists in the world working in Britain.
"We need artists' unique perspectives on the on the enormous challenges facing us."
Hiorns's work included a melted passenger jet engine and an untitled steel frame filled with cows' brains. He had been the bookmakers' favourite.
David's work includes pictures of unclothed dolls, whilst Skaer's entry features 26 sculptures made from coal dust.
Previous winners of the prize include Martin Creed, Grayson Perry, Gilbert and George, and Damien Hirst.
The judges for this year's prize included broadcaster Mariella Frostrup, art critic Jonathan Jones and Dr Andrea Schlieker, director of the Folkestone Triennial art exhibition.
Last year, Mark Leckey won with a pop culture influenced film featuring Homer Simpson and Felix the Cat.
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