According to biographer Kevin Belmonte, there are only two surviving recording of D. L. Moody’s voice. One is of him reading the Beatitudes; the other is of him reading from Psalm 91.
I’ve only been able to locate the former. Recorded in 1898, Moody would have been 61 years old at the time. He died on December 22, 1899, missing the 20th century by just over a week.
The recording is of poor quality:
Moody Bible Institute also has a recording of an audio clip of Moody’s friend and song leader Ira Sankey singing, “God Be with You.”