Mitchell says the camera was a gift from NASA. In March, he tried to auction it through the British firm Bonhams. NASA says the camera is U.S. government property.
In papers filed Thursday, the U.S. Attorney's Office in Miami stated Mitchell will agree to return the camera to NASA. NASA will in turn give it to the National Air and Space Museum in Washington for display.
A judge must sign off on the settlement.
The camera was one of two 16 mm motion picture cameras on the spaceship.
Mitchell is one of 12 humans to walk the moon. He also received the Presidential Medal of Freedom.