"They are marked and ready to go to their destinations. They are awaiting the next aircraft," said airline spokeswoman Andrea Huguely.
The malfunction on Wednesday led to five cancellations and delays averaging 90 minutes on 48 flights out of JFK's Terminal 8.
Six more flights were canceled early Thursday before the system was restored.
Airline officials said technicians, after struggling for hours, traced the problem to the baggage sorter's communication network.
The system is only a year old.
On Wednesday, thousands of customers had to fly to their destinations without their luggage, and hundreds of bags accumulated in the terminal lobby after the automated sorter stopped working at 4:45 a.m.
With the system down, airline employees had to sort each bag by hand. Even with extra helpers pitching in, they couldn't keep up with the flood of luggage.
American gave passengers the choice of waiting out the problem, traveling from another area airport or flying on and having their bags delivered later.
Because of the crisis, American waived its fees Wednesday for travelers checking fewer than three bags at JFK. Starting in June, the airline, like most of its competitors, has charged $15 for one checked bag or $40 for two bags. Passengers may still carry on luggage for free.
The airline noted that a majority of the flights affected by Wednesday's baggage problem were international and thus not subject to the fees in the first place.