The winner was unveiled during a live televised broadcast by Irish actress Saoirse Ronan, from Derry's Ebrington Square.
Nominees have had their works on display since October, with free public entry to the four finalists.
The Turner Prize has travelled outside England for the first time and will continue to be on show until January 5.
Ghanaian Lynette Yiadom-Boakye is the first black woman to be in contention for the Turner Prize award.
Her portraits of six imaginary people use invented pre-histories and are aimed at generating questions about how pictures are read in general.
The bookies' favourite to win was Glasgow-based artist David Shrigley, whose piece Life Model features a larger-than-life and disproportionate naked male robot.
One of the best-known artists in the running for the £25,000 prize money is Berlin-based Tino Sehgal, 37, whose work This Is Exchange consists of live "encounters" between interpreters dressed in black T-shirts and the audience.
Sehgal's nomination is the first time a live, partially structured exhibition has been included in the Turner Prize shortlist.
Established in 1984, the Turner Prize is awarded to a contemporary artist under 50, living, working or born in Britain, who is judged to have put on the best exhibition of the last 12 months.
Previous winners include Damien Hirst and Tracey Emin and short-listed nominees receive £5,000 prize money.
The exhibition for the prize, which has travelled outside England for the first time, will be staged in Ebrington Army barracks, a former military barracks, in the city until January 5.
This year's judges were Ralph Rugoff, the director of the Hayward Gallery, London, Declan Long from the National College of Art, Dublin, Annie Fletcher, from the Eindhoven's Van Abbemuseum, and Susanne Gaensheimer from the Museum of Modern Art in Frankfurt.