Middle English prechen, "deliver a sermon, proclaim the Gospel," from late Old English predician, a loan word from Church Latin; reborrowed 12c. as preachen, from Old French preechier "to preach, give a sermon" (11c., Modern French précher), from Late Latin praedicare "to proclaim publicly, announce" (in Medieval Latin "to preach," source also of Spanish predicar), from Latin prae "before" (from PIE root *per- (1) "forward," hence "in front of, before") + dicare "to proclaim, to say" (from PIE root *deik- "to show," also "pronounce solemnly," and see diction). Related: Preached; preaching.
Meaning "give earnest advice, especially on moral subjects" is by 1520s. To preach to the converted is recorded from 1867 (the form preach to the choir attested from 1979).