After Morgan acquired the tape, he sold it to magician David Copperfield, who then donated it to the National Civil Rights Museum to promote King's message of nonviolence.
Copperfield said King inspired people to dream.
"That's too important for one person to possess," Copperfield said of the recording. "You have to share that with people to remind as many people as possible of the message."
Barbara Andrews, the museum's director of education, said she's pleased the museum's visitors will get a chance to hear the recording, which will be among the exhibits at the newly-renovated facility scheduled to fully open in April.