Short answer
– The most likely author is the prophet Jeremiah himself, with Baruch son of Neriah acting as his scribe/amanuensis. Evangelical Christians typically affirm Jeremiah as the primary author of the material in Jeremiah 29, including verses 11–13.

Why evangelicals say Jeremiah is the author
– The text itself identifies the origin: Jeremiah 29:1 introduces the passage as “the words of the letter that Jeremiah the prophet sent from Jerusalem to the surviving elders… and to the priests…” (ESV/NIV-type wording).
– The book of Jeremiah elsewhere describes Jeremiah dictating his messages to Baruch, who wrote them down (see Jeremiah 36). Evangelicals therefore see Jeremiah as the prophetic source and Baruch as the one who physically wrote and preserved the text.

Historical context (brief)
– Jeremiah prophesied in Judah during the late 7th and early 6th centuries BC (roughly 627–586 BC), across the reigns of Josiah and the last kings of Judah and through the Babylonian exile.
– Jeremiah 29 is presented as a letter to Judean exiles living in Babylon, addressing their situation in exile and God’s long-term plans (including the 70‑year word in Jeremiah 29:10).

Evangelical theological emphases about the author and passage
– Prophetic authorship: evangelicals affirm Jeremiah as a genuine prophet called by God (Jeremiah 1) whose words carry divine authority.
– Authenticity and trustworthiness: because Jeremiah is seen as the prophet-author and his scribe Baruch is named in the narrative, evangelicals treat the passage as authoritative Scripture, historically situated but spiritually relevant today.
– Contextual reading: evangelicals often point out that Jeremiah 29:11–13 are part of a pastoral letter to an exiled community (promising restoration and calling them to seek the Lord), and they encourage applying the passage faithfully (not turning it into a vague personal prosperity promise detached from its context).

Practical note
– Many evangelical teachers draw from Jeremiah 29:11–13 encouragement that God knows and works out a hopeful plan for his people and that God can be sought and found; at the same time they commonly stress reading the verses in their original context (a letter to exiles) and recognizing Baruch’s role as Jeremiah’s scribe in the book’s transmission.

If you’d like, I can: provide the relevant cross-references (Jeremiah 36, Jeremiah 1), give a short outline of Jeremiah’s life and ministry, or point to a few evangelical commentaries that treat Jeremiah’s authorship and the letter to the exiles.