He added: "This is good, it's good, it's a good thing."
His winning works include the film Cinema in the Round which shows him lecturing about his love of animation.
The key motifs of the work of Leckey, who creates footage based on contemporary culture, are desire and transformation.
According to judges, he uses his "own state of being" - an artist in London who grew up in northern England in the 1980s - to explore those motifs.
"He celebrates the imagination of the individual and our potential to inhabit, reclaim or animate an idea, a space, or an object," they added.
The artist was shortlisted for solo exhibitions Resident, at Kolnischer Kunstverein, Cologne, and Industrial Light & Magic, at Le Consortium, Dijon.
Leckey, the bookmakers' favourite, was the only man on the shortlist
Leckey, the only man on the shortlist, beat Goshka Macuga, Runa Islam and Cathy Wilkes to win the prize, which has had only three female winners since its 1984 inception.
He had been favourite with bookmaker William Hill at a price of evens to win the prize, awarded annually to an outstanding body of work by an artist "under 50, born, living or working in Britain".
Glasgow-based Wilkes had been shortlisted for works including a female mannequin sitting on the toilet with pieces of wood and horseshoes tied to her face.
She was nominated for her solo exhibition at Milton Keynes Gallery, described by the Tate as touching "on issues of femininity and sexuality".
Textile displays
Polish-born Macuga, 41, works as a "cultural archaeologist".
The Tate had said she "merges the roles of collector, curator and artist" to create dynamic - and often theatrical - sculptural installations.
She had recreated textile displays made 80 years ago by modernist designer Lilly Reich, using original drawings and photographs.
This year's Turner Prize exhibits
Works by Islam, 38, who was born in Bangladesh and lives and works in London, included the film, Be The First To See What You See As You See It (2004).
It has a woman dressed in white wandering around a gallery space of fragile porcelain pieces, before throwing them to the floor.
The Tate described her as exploiting classic cinematic techniques in her work - such as lighting, colour and cinematography - in order to invite an emotional response from the viewer.
The work of all four shortlisted artists has been on display at Tate Britain since the end of September.
The Turner Prize has been traditionally won by controversial works.
Previous winners have included transvestite potter Grayson Perry, Damien Hirst, and Gilbert and George.
Last year's winner, Mark Wallinger, took the prize for his replica of Brian Haw's anti-war protest in Parliament Square, London.
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