The book of Exodus contains specific statements that point to Moses as its author. Moses, for example, wrote about the battle against the Amalekites “in a book” (Exodus 17:14). Also Numers 33:2, points to the fact that Moses had a diary where he kept record of certain events.
In addition, it is clear from Exodus 24:4 that Moses wrote down the ordinances contained in Exodus 20:21 to Exodus 23:33, the “book of the covenant” (Exodus 24:7). And according to Exodus 34:27, Moses is the author of the revelation recorded in Exodus 33:11–26. The evidence that is found in the book of Exodus points specifically to Moses as the author of historical and other reports found in it. Except for Moses, no individual is mentioned in the Pentateuch as having written any part of it.
Another proof for the authorship of Moses, is the use of many Egyptian words and the correct description of the Egyptian life. All these facts that are recorded in the first part of the book keenly show that the author had been learned in Egypt and was closely familiar with the land and its customs. No other known Hebrew person after Joseph was capable to record the story of the Exodus. Moses alone seems to have been “learned in all the wisdom of the Egyptians” (Acts 7:22).
But the most decisive evidence of the Mosaic authorship is given in the New Testament. In Mark 12:26 Jesus quotes from Ex. 3:6, and says that His source is the book of Moses. Jesus said, “But concerning the dead, that they rise, have you not read in the book of Moses, in the burning bush passage, how God spoke to him, saying, ‘I am the God of Abraham, the God of Isaac, and the God of Jacob’?”
The above three points—the straight testimony of the book itself, the secondary proof that the author was learned in Egypt, and the direct testimony of Christ—all these pledge for the correctness of the Jewish tradition that Moses is the author of the book of Exodus.
In His service,