Entitled "Such Tweet Sorrow," the experiment is a collaboration between the Royal Shakespeare Company (RSC) and Mudlark, which produces entertainment on mobile telephones.
Organizers have already outlined a contemporary "narrative arc" loosely based on the original tragedy, and the cast will improvise the rest through Tweets which have already begun to appear on the website www.suchtweetsorrow.com.
The production will take place over five weeks and allows for the characters to interact not only among themselves but also with members of the "audience."
Each character writes their own tweets, guided by an existing storyline and diary which outlines where they are at any moment in the adventure.
And so two families named after the original adversaries the Montagues and Capulets have loathed each other for years after a fatal car crash in an unnamed English market town in 2000.
Juliet, played by actress Charlotte Wakefield, is just turning 16 and wonders whether she should have a birthday party to celebrate. She posts a video on Youtube showing viewers a typical teenager's bedroom.
Her Twitter name is @julietcap16 while Romeo's entry into the messaging world comes later as "he is too busy on his Xbox."
"We have no real idea of what the next five weeks will bring, but we are holding onto our seatbelts," said Charles Hunter from Mudlark.
Michael Boyd, artistic director of the RSC, added: "Our ambition is always to connect people with Shakespeare and bring actors and audiences closer together.
"Mobile phones don't need to be the antichrist for theater. This digital experiment ... allows our actors to use mobiles to tell their stories in real time and reach people wherever they are in a global theater."