The planes to be used have undergone the updates required by the US Federal Aviation Administration to end a long grounding after two flights crashed killing 346 people.
In granting approval for the Max charters, the regulator also authorised American to begin revised pilot training before changes to its flight manual take effect December 22.
'We know that restoring our customers' confidence in the 737 Max starts with ensuring our own team members are comfortable,' the airline said in a message on its internal computer network. American also said it's planning opportunities for corporate customers to see the aircraft and ask questions.
The F cleared the Max to resume flying on November 18, having mandated new pilot training and changes to a safety system linked to the crashes in Indonesia.
American has scheduled the first domestic service with single daily round trips between Miami and LaGuardia from December 29 through January 4.