Responding to the news, Zegler said: “Well… hello to a dream come true.”
Snow White And The Seven Dwarves, released in 1937, was the first Disney animated feature film.
It tells the story of a princess fed a poisoned apple by her stepmother, placing her in a deep sleep from which she can only be awakened by a kiss from a prince.
Its original soundtrack includes the songs Heigh-Ho, Someday My Prince Will Come and Whistle While You Work.
Marc Webb, whose previous films include 500 Days of Summer and The Amazing Spider-Man, is set to direct the live-action version.
He said he was “thrilled” at Zegler’s casting.
Production on Snow White is expected to begin next year.
Disney finds its Snow White for live-action adaptation of classic fairytale