The combined carrier will be called American Airlines but run by US Airways CEO Doug Parker.
The boards of the two airlines unanimously approved the deal late Wednesday, and the companies announced the agreement Thursday.
The merger would reduce the number of major U.S. airlines to four: the new American, United, Delta and Southwest.
The deal is a coup for smaller US Airways Group Inc., which pushed for a merger almost as soon as American parent AMR Corp. filed for bankruptcy protection in November 2011.
While Mr Parker runs the company, AMR CEO Tom Horton will serve as chairman until its first shareholder meeting, likely in mid-2014.
"The combined airline will have the scale, breadth and capabilities to compete more effectively and profitably in the global marketplace," Mr Parker said in a statement. "Our combined network will provide a significantly more attractive offering to customers, ensuring that we are always able to take them where they want to go."
AMR creditors and shareholders including creditors will own 72 per cent of the new company and US Airways shareholders 28 per cent.
The companies said merging would create savings of more than $1 billion a year. The merger will be part of AMR's plan for exiting bankruptcy protection.
The airlines said they expect $1 billion in combined savings.
The companies had negotiated since August, when creditors pushed AMR to conduct merger talks so they could decide which earned them a better return: a merger or an independent American.
The deal would need approval by AMR's bankruptcy judge and antitrust regulators, who have permitted three other big airline mergers to go ahead since 2008.
The rapid consolidation has allowed the surviving airlines to offer bigger route networks that appeal to high-paying business travelers. And it has allowed them to limit the supply of seats, which helps prop up fares and airline profits.
The new American would 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, not counting regional affiliate airlines.