Short answer: Evangelical Christians generally identify Moses as the most likely human author of Deuteronomy 18:15. Deuteronomy itself is presented as Moses’ farewell address to Israel, and both Jewish and Christian tradition (including the New Testament) treat Moses as the speaker.

Why evangelicals say “Moses” (summary)
– Internal testimony: Deuteronomy is written in the first person with Moses repeatedly presented as the speaker and lawgiver (Deut. 1–34). Verse 18:15 falls inside Moses’ farewell speeches.
– Traditional witness: Jewish tradition, the early church, and the historic Christian confession attribute the Pentateuch (the first five books, including Deuteronomy) primarily to Moses.
– New Testament affirmation: Jesus’ followers and the apostles quote Deut. 18:15 as part of Moses’ prophecy (see Acts 3:22–23 and Acts 7:37), treating the verse as Moses’ own word and pointing to a greater fulfillment in Christ.
– Evangelical confidence in inspiration: Because evangelicals hold the Old Testament as divinely inspired and authoritative, they generally accept the book’s own presentation unless there is strong reason to reject it.

Notes about scholarly nuances (how many evangelicals qualify the simple view)
– Many conservative evangelicals still allow for editorial activity—minor later additions, copying, or arrangement—without denying Moses as the principal author or source of Deuteronomy’s core teaching. Some would say Moses wrote the bulk of the book and later scribes or the Deuteronomic school may have preserved or finalized the text.
– A smaller number of evangelical scholars engage seriously with critical proposals (e.g., Deuteronomistic editing or later composition) and offer various reconciliations that still affirm Moses’ foundational role.

Why this matters for evangelicals
– Seeing Moses as author preserves the continuity of God’s revelation through Israel’s law and links Moses’ prediction (“a prophet like me”) with New Testament claims about Jesus (the NT cites Deut. 18:15–19 in connection with Christ).
– It supports evangelical convictions about Scripture’s reliability and across-testament unity: God’s redemptive plan hinted in the Torah comes to fuller expression in the New Testament.

For further reading (evangelical-friendly)
– Daniel I. Block, commentary on Deuteronomy (NICOT).
– Walter C. Kaiser Jr., work on Old Testament theology and the Pentateuch.
– John Sailhamer, The Pentateuch as Narrative (nuanced, conservative).
– Acts 3:22–23 and Acts 7:37 for the New Testament’s use of Deut. 18:15.

If you want, I can:
– Summarize the passage’s immediate literary context,
– Show how New Testament writers apply it to Jesus,
– Or give short bios and positions of specific evangelical scholars on Mosaic authorship.