"This partnership with Miramax is a unique creative and business opportunity to own what we create and to expand our vision into other media," Brown said in a statement issued jointly with Miramax, a subsidiary of Walt Disney Co.
The new company will publish a monthly magazine, produce films and TV programming, and publish books. Brown will serve as chairman.
Ron Galotti, publisher of Vogue, which like The New Yorker is owned by Conde Nast Publications, also resigned to join Brown as president of the new company.
Harvey Weinstein, Miramax co-chairman, said the new venture "fulfills my goal of producing a dramatic Act Two for Miramax by entering exciting new areas of creativity with two tremendous partners."
He praised Brown as "an innovator who revolutionized the magazine business at both Vanity Fair and The New Yorker."
Brown took over the literary and current-events magazine with much fanfare in September 1992. Since then, she has won both praise and criticism for her efforts to update it, maintaining a generally literary focus while adding photographs, beefing up coverage of politics and popular culture, and shortening articles.
She said her decision to leave "is no reflection on my wonderful experiences with Conde Nast."
She previously served as the high-profile editor of Vanity Fair, another magazine owned by Conde Nast.
The New Yorker has a circulation of about 800,000.
The parent of Conde Nast, Advance Publications, whose chairman is S. I. Newhouse Jr., bought the magazine in 1985 for $168 million. While circulation has grown steadily in the last six years, the business side has struggled.
Last year, the magazine lost around $10 million.
Brown's resignation comes as Conde Nast begins to fold the magazine into the operations of its other 15 publications - including Vogue and Vanity Fair - to economize on expenses. The merger will enable Conde Nast to package The New Yorker with its other publications and offer advertisers bulk corporate rates.
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