Iger is due to take up the role in September this year but has worked alongside Eisner at Disney since 2000 as its president and chief operating officer.
His election as chief executive culminates a selection process that started in September last year when Eisner announced his retirement.
George Mitchell, chairman of The Walt Disney company board of directors, said: "Bob is an experienced, talented and visionary leader who has made crucial and substantial contributions toward Disney's strong performance. I want to express how excited we are at the prospect of Bob leading this extraordinary company and talented management team to new levels of financial and creative success in the years ahead."
Iger's management career at Disney began nine years ago and since then he has worked as the chairman of Disney-owned ABC Group, where he guided the merger of ABC with The Walt Disney Company. He was also the president of Walt Disney International.
Before that he was executive vice-president of the ABC Television Network, becoming president of ABC Entertainment in Los Angeles a year later. He has also worked as vice-president of programming at ABC Sports, starting out as a studio supervisor at ABC in 1974.
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