“These are hard jobs to leave,” said Michael Nathanson, a veteran Hollywood analyst and partner at MoffettNathanson. “Look at Disney’s peer group among big media companies. Most of them had chief executives that didn’t leave by choice and didn’t leave when they were as young as Bob.” (Mr. Iger is 64.) “He’ll go out on top, and he’ll go out on his own narrative. He deserves a lot of credit for that.”

For many chief executives, the ability to exit gracefully while anointing a strong successor is one of the most important but least appreciated qualities of leadership, according to David Larcker, a professor at the Stanford Graduate School of Business and an expert in corporate governance. “It’s very difficult,” he said. “Look at Ovitz at Disney. That was a monumental disaster. And the transition from Eisner was awkward, to put it mildly. You have to admire Iger, who recognized that he’s done what he came to do and it’s time for new blood. From the outside, this appears to be going very smoothly. Disney has successfully avoided any public spectacle.”

Five years ago, Mr. Iger had Mr. Staggs and Mr. Rasulo switch jobs, naming Mr. Staggs head of Disney’s theme parks and resorts, and Mr. Rasulo chief financial officer. Mr. Staggs worked at Morgan Stanley before joining Disney in 1990 in strategic planning, but lacked operational experience. Mr. Rasulo also started in strategic planning in 1986 after working at the Marriott Corporation, and ran the troubled Disneyland Paris before becoming chairman of parks and resorts. He was seen as needing Wall Street exposure.

Judson Green, who worked closely with both men during his 10 years of running Disney’s parks and resorts division, said both were strong candidates. “Bob had an embarrassment of riches,” he said, and still has three years to make a final decision. But of the two, “Bob may have felt that Tom is a little more polished, a little more charismatic. He has great presentation skills and is a little more Disney-like than Jay.” At age 54, Mr. Staggs is also a few years younger.

A current Disney executive said people inside the company were enthusiastic about Mr. Iger’s choice, with the exception of some loyalists to Mr. Rasulo, and were glad the contest was over. “It was awkward and sometimes tense,” said this person, who spoke on the condition of anonymity. Mr. Staggs “is very artist-friendly. He’s a musician. He’s warm and friendly, and he’s got a gorgeous family.” (People told me Mr. Staggs is an accomplished trumpet player.)