Mr Bachchan's role will be a supporting one, Shantaram will mark his first international movie.
The new venture coincides with Warner Bros. Pictures giving Graham a three-year extension of his overall production deal, as well as the extension of his deal with Depp's Infinitum Nihil.
The news came as The Departed producer completed meetings at Cannes to finalize the project, amcTv.com reports.
According to Variety magazine, under the new deal, not only will Warner Bros. get first choice of films produced under the GK Films moniker, including titles from Johnny Depp's Infinitum Nihil label, but also titles developed and produced under the Initial Entertainment banner.
King however will continue as the principal in Initial Entertainment as the proxy-CEO.
The first movie to be produced under the GK banner will be The Young Victoria starring Emily Blunt.
The film will be directed by Canadian director Jean Marc Vallee and will begin shooting in August.
Also in the pipeline is The Invention of Hugo Cabret which will be produced for Warner Bros, and is slated to be directed by Martin Scorsese.
The film is reportedly based on a bestseller by Brian Selznick and the script has been written by John Logan.