DALLAS >> American Airlines and US Airways will merge and create the world’s biggest airline. The boards of both companies approved the deal late today, according to four people close to the situation.

The carrier will keep the American Airlines name but will be run by US Airways CEO Doug Parker. American’s CEO, Tom Horton, will serve as chairman of the new company until mid-2014, these people said. They requested anonymity because the merger negotiations were private.

The merger caps a turbulent period of bankruptcies and consolidation that will leave the U.S. airline industry dominated by four big carriers — American, United, Delta and Southwest. Together they would control almost three-quarters of U.S. airline traffic.

The deal has been in the works since August, when creditors forced American to consider a merger rather than remain independent. American has been restructuring under bankruptcy protection since late 2011. AMR creditors and possibly its shareholders will own 72 percent of the stock, and US Airways Group Inc. shareholders will get the rest, three of the people said.

A formal announcement is expected Thursday morning.

If the deal is approved by American’s bankruptcy judge and antitrust regulators, the new American will have more than 900 planes, 3,200 daily flights and about 95,000 employees, not counting regional affiliates. It will be slightly bigger than United Airlines by passenger traffic.

Travelers on American and US Airways won’t notice immediate changes. It likely will be months before the frequent-flier programs are merged, and possibly years before the two airlines are fully combined.

When that happens, American’s presence will grow in key East Coast markets including New York’s LaGuardia Airport and Washington’s Reagan National Airport. The merger will add US Airways hubs in Charlotte, Philadelphia and Phoenix to American’s in Dallas-Fort Worth, Chicago, Miami, New York and Los Angeles.

US Airways would boost American’s service to Europe and the Latin America-Caribbean market but wouldn’t fix American’s weakness on routes to Asia.

Just five years ago, American was the world’s biggest airline. It boasted a history reaching back 80 years to the beginning of air travel. It had popularized the frequent-flier program and developed the modern system of pricing airline tickets to match demand.

But years of heavy losses drove American and parent AMR Corp. into bankruptcy protection in late 2011. The company blamed bloated labor costs; its unions accused executives of mismanagement.

The merger is a stunning achievement for Parker and his management team at US Airways, based in Tempe, Ariz. Just a few years ago, they were running a mid-sized carrier called America West Airlines when they bought the old US Airways out of bankruptcy.

Parker’s airline is only half the size of American and is less familiar around the world, but he prevailed by driving a wedge between American’s management and its union workers and by convincing American’s creditors that a merger made business sense.

Despite its smaller size, US Airways has prospered in the last several years, earning a record profit of $637 million last year.

“They’ve done an absolutely terrific job with what they have,” said Bill Swelbar, an airline-industry researcher at MIT and board member of Hawaiian Airlines’ parent company.

Parker began pursuing a merger almost as soon as AMR filed its Chapter 11 petition. He found willing partners in American’s three labor unions, who have long fought with management at their own company over pay, work rules and executive bonuses. American suffered strikes by pilots and flight attendants in the 1990s. Bad feelings hardened in the early 2000s, when union workers took pay cuts to keep the company out of bankruptcy while AMR gave bonuses to management employees when the stock price rose.

AMR’s Horton professed no interest in thinking about a merger until his company was out of bankruptcy court, but his creditors pressured him to reconsider. AMR lost more than $12 billion between 2001 and 2010. It has lost another $2.8 billion since it filed for bankruptcy protection in November 2011 — a period in which US Airways earned about $650 million. Some analysts and creditors called for new management at AMR.

Bob Herbst, a financial analyst who studies airlines, said AMR has failed to adapt to changes in the industry since consolidation began in the middle of the last decade. He said AMR was fixated on gaining market share rather than on profitability.

American ranked 14th out of 15 airlines in government rankings for on-time performance in 2012 (US Airways was fifth). Only United had a higher rate of complaints (but US Airways was barely better than American).

“They are continually at the bottom in on-time and customer service, and they’re losing more money than anyone else,” Herbst said. “American’s management is leaving because that’s what needs to happen.”

AMR, however, has made measurable progress under Horton, who became CEO the day before the company filed for bankruptcy protection. The company earned operating profits in the second and third quarters of 2012, and its revenue for every seat flown one mile — an arcane-sounding statistic but one that is closely watched in the airline business — rose faster than at its rivals for much of the year. With leverage from bankruptcy laws, AMR won new union contracts with lower costs.

“I’m a big fan of Tom’s; he’s done a great job,” said Mike Derchin, an analyst with CRT Capital Group. “He restructured the balance sheet, made the company more efficient and got a pilots’ contract. He positioned the company for the future.”

That performance may also have gotten a better deal for Horton’s creditors. US Airways’ initial proposal called for AMR creditors to get only 49 percent of the stock in the combined company, according to people familiar with the talks. Instead, they’ll get 72 percent, although they might have to share some of that with shareholders, said the people familiar with the deal.

In recent weeks, AMR won bankruptcy court approval to buy hundreds of new planes from Boeing and Airbus, an important step to reduce fuel costs and offer a more comfortable experience for passengers. American even unveiled a new logo and paint job for its planes, although the reviews were mixed.