Boeing’s deepest problem in 2005 was a universal one: No empire rises forever. The company had been floundering, and the digital revolution was barging down the gangway. The board figured it was time to buckle up.

The tricky thing about reforming Boeing was the weight of its heritage. Many of its veteran engineers and machinists viewed technological innovation as a higher calling, a culturally inviolable pursuit.

In theory, there may be a gradual way to renovate a proud old institution, but that’s rarely how it happens. History shows that it usually comes down to one determined individual—someone who bursts through the door swinging a 7-iron.

Mr. McNerney had never worked at Boeing—he wasn’t even an engineer. His operational religion, honed at 3M and General Electric , ran toward ethics, production efficiencies and cost cutting.

“Boeing was a great company but we’d lost our way culturally,” he said in a recent interview. “It needed to regain confidence.”

Disruptive leadership has become a less novel concept for most Americans, given the modus operandi of President Donald Trump. The business world, by contrast, has met these folks before, whether it was Arthur “the Ax from Saks” Martinez at Sears, “Chainsaw” Al Dunlap at Sunbeam, Steve Jobs at Apple , Ron Johnson at J.C. Penney, Marissa Mayer at Yahoo or John Flannery’s early work at GE.

Liz Wiseman, who studies “high-impact” leaders, divides them into “multipliers” and “diminishers.” Both species embrace conflict, are ruthlessly direct and intellectually irreverent. The major difference, she says, is intent.

A multiplier’s goal is to light a fire that helps people think big (Apple’s Mr. Jobs comes to mind). A diminisher uses disruption as a means of self-aggrandizement, which can lower performance.

“Sometimes you need someone who’s a bit of a wrecking ball,” Ms. Wiseman says, “but we also need leaders who can draw on the capability of the team.”

Depending on whom you ask at Boeing, Mr. McNerney might land in either category. The company he inherited was reeling from a series of military procurement scandals, and his opening salvo was an ethical crackdown. Next came noisy moves such as cutting jobs, streamlining production and pressuring suppliers on cost.

As the company scrambled to absorb these reforms and deliver its next-generation 787 Dreamliner, Mr. McNerney infuriated many proud engineers by outsourcing some of the aircraft’s most sophisticated components. This decision set the stage for the bumpiest patch of his tenure.

Complications from outsourcing played a role in delaying the 787’s launch by more than three years, and the fleet was later grounded for a time when its lithium-ion batteries caught fire. Flipping on his office television one day in 2013, Mr. McNerney saw firefighters rushing into a smoking Dreamliner at Boston’s Logan Airport. Eight days later, a planeload of passengers in Japan had to barrel out of a 787 on emergency slides.

Critics said Boeing was trying to do too many new things at once. Mr. McNerney later said the company’s obsession with pursuing ambitious technological “moonshots” had compounded its risk.

His move to eliminate thousands of jobs sparked years of clashes with labor unions. The nadir came in 2014, when he joked about the company’s employees “cowering” before him. He later apologized.

From 2007 to 2011, as it weathered internal turmoil and the global financial crisis, Boeing’s revenue remained flat. By 2014, however, thanks to surging global demand for commercial jets, it had climbed to a record $90.8 billion. The following year, Boeing’s share price hit an all-time high. Over Mr. McNerney’s full 11-year tenure, Boeing’s stock handily outperformed the S&P 500.

The company’s workers never did warm up to the boss. When he retired in March 2016, one union official issued a frosty statement. It began: “CEOs come and CEOs go...”

As Mr. McNerney sees it, these sore feelings had less to do with his personal style than the difficulty of what needed to be done. “The act of leadership is not always comfortable,” he said.

Nonetheless, he added, “I didn’t try to confront people with their shortcomings. I tried to remind them what made them great and reconnect them to it.”

It can be hard to say whether a CEO’s bold actions genuinely changed the outcome, or even whether they suited the gravity of the circumstances. It also seems unfair to grade these leaders in isolation. At Boeing and many other mature companies shaken up by disrupters, a lot depends on who comes next.

Dennis Muilenburg, Boeing’s current CEO, was Mr. McNerney’s handpicked successor and, in many ways, his opposite. A low-key engineer who joined the company as an intern, he made a point of spending time talking to workers—a contrast to his predecessor, who was often viewed as personally remote.

He continued reducing union jobs but softened the blow by focusing on voluntary buyouts and attrition, and finalized a long-term contract with the engineers. In a nod to the “old” Boeing, he insisted that the most technologically forward features of the next-generation 777X would be designed and manufactured in-house.

When President-elect Trump in late 2016 posted tweets threatening to cancel Boeing’s Air Force One contract over costs he deemed “out of control,” the new CEO didn’t bristle. He quietly picked up the phone and hashed out a better deal.

In 2017, aided by stock buybacks, roaring demand and an impending tax cut, Boeing’s share price nearly doubled. The company delivered a record 763 jets, recorded $13.3 billion in operating cash flow and paid out the largest employee bonuses in its history.

Mr. McNerney’s hard-fought reforms clearly played a role, but only to a point. Unlike many chief executives who’ve followed disruptive acts, Mr. Muilenburg avoided two classic mistakes. He didn’t maintain the same turbulent course—that almost never works. Critically, however, he also didn’t try to put everything back the way it was.

By adopting a muted style and making a few cultural readjustments, Mr. Muilenburg banked a load of goodwill. He spent this capital to continue implementing his predecessor’s best ideas.

What Boeing’s story suggests is that the turbulent stretch of the journey doesn’t define the flight. The climactic event is picking the next pilot.

“If a leader comes in and reorients and disrupts and isn’t followed by someone who can build on that and further improve the culture, everything falls back,” Mr. McNerney says. “I think the board did a great job picking someone like Dennis to follow someone like me.”

—Mr. Walker, a former reporter and editor at The Wall Street Journal, is the author of “The Captain Class: The Hidden Force That Creates the World’s Greatest Teams” (Random House).

Write to Sam Walker at sam.walker@wsj.com