The 26-year-old actress will portray the iconic performer in both the movie and stage adaptations of Gerald Clarke’s biography Get Happy: The Life of Judy Garland.
Harvey Weinstein, of The Weinstein Company who secured the film and stage rights of the book, is delighted to have Anne on board.
He said: "We are thrilled to have the brilliantly talented Anne Hathaway portray stage and screen legend Judy Garland. I have worked with Anne on projects in the past and have known her for many years. She will be a true class act in this challenging role.
"Gerald Clarke's biography is a fascinating and comprehensive look at Garland's life and is particularly outstanding because of its exclusive details from her own writings. Her story is incredible subject matter for both theatre and film and we look forward to bringing it to audiences."
It is unclear whether the stage production or movie will be produced first. Former child star Judy, the mother of actress Liza Minnelli, battled a string of addictions and attempted suicide several times.
The Wizard of Oz star married five times and suffered financial problems throughout her career.
Judy died of an accidental drugs overdose in 1969 at the age of 47.