The airline said it worked with the Allied Pilots Association to cover the unmanned flights and ensure they will operate as scheduled.
"By working together, we can assure customers that among the many stresses of the season, worrying about a canceled flight won't be one of them," the airline said in a statement.
"Much appreciation to APA President Capt. Dan Carey and our 15,000 professional aviators who are doing their part to cover the holiday schedule and beyond," the company added.
The APA released a statement saying in part, "With this agreement in principle, we anticipate that American Airlines will be able to maintain a full December schedule as planned for its passengers."
The scheduling glitch had left American scrambling for pilots to cover thousands of flights over the Christmas holiday period.
Pilots bid each month for flying assignments based on seniority. The scheduling glitch let pilots drop scheduled flights - to take a vacation over Christmas, for example - even when there were no other pilots available for that flight. Normally such a request would be denied, especially during busy travel periods.
The pilots' union estimated that when the problem was discovered late last week, about 19,000 cockpit seats were left empty. The glitch affected flights between Dec. 17 and Dec. 31 from nearly a dozen airports including hubs in Dallas, Chicago and Miami.
The Associated Press contributed to this report.