Price was one of two film and video artists among the finalists, along with Scotland's Luke Fowler.
The Turner Prize, named after 19th-century landscape painter J.M.W. Turner, was established in 1984 to honor younger British artists.
It often sparks heated debate about the value of modern art. Past winners include transvestite potter Grayson Perry, dung-daubing artist Chris Ofili and shark pickler Damien Hirst.
This year, most media attention had focused on pop-performance artist Spartacus Chetwynd, who creates carnival-style spectacles inspired by everything from Michael Jackson's music to "Star Wars" character Jabba The Hutt, and illustrator Paul Noble, who produces drawings of a dystopian imaginary city populated by human excrement.
Work by the four finalists is on show at Tate Britain until Jan. 6.