Hepburn's LBD is perhaps the most famous outfit in the Hollywood history while Stone's character wore the white dress in the infamous interrogation scene with Michael Douglas leading to speculation that she was not wearing any underwear.
These dresses are part of a collection of famous outfits spanning a century of films and will be on show at V&A museum here, the Daily Mail reported.
Judy Garland's pinafore from her role as Dorothy in the 'Wizard of Oz' will also be on display.
Other iconic costumes at the exhibition are Marilyn Monroe's sheer white cocktail dress from 'Some Like It Hot' and Meryl Streep's outfits from when she portrayed Margaret Thatcher in the 2011 film 'The Iron Lady'.
Christian Bales' Batman suit from this year's hit 'The Dark Knight Rises' and Daniel Radcliffe's Gryffindor school uniform from his role as Harry Potter are also going on show.
The collectors who have loaned to the exhibition range from major motion picture studios, costume houses, public museums and archives and private individuals.
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Other famous costumes include those from such films as 'Fight Club', 'Indiana Jones: Raiders of the Lost Ark', 'the Addams Family', 'The Last Emperor' and 'Brokeback Mountain'.
Also on show are costumes from 'Cleopatra', 'Ben Hur', 'True Grit', 'Star Wars', 'Who Framed Roger Rabbit' and 'Avatar'.