The book's writer EL James told fans the news on Twitter.
The novel, the first of a trilogy of steamy tales dubbed ''mummy porn'', has become a literary phenomenon, selling more than 5.3 million copies to become the best-selling book of all time in the UK.
James wrote: "I'm delighted & thrilled to let you guys know that Sam Taylor-Johnson has agreed to direct the film of Fifty Shades Of Grey."
Taylor-Johnson is one of the leading names in contemporary British art and won praise for her feature film debut Nowhere Boy in 2009, the story of the early life of John Lennon. It starred young actor Aaron Johnson, whom she married last year despite being 23 years his senior.
She is well known for her videos and photography, including a famous work in which she filmed David Beckham asleep.
In 2006 she made a short film which featured a man masturbating in the middle of Death Valley.
The artist - who lost out to Chris Ofili when she was shortlisted for the Turner in 1998 - also made Crying Men, a film in which a number of Hollywood stars are shown in tears.
Taylor-Johnson - who has twice overcome battles with cancer - was married to art dealer Jay Jopling for 11 years, splitting in 2008.