"one who changes from one sect, creed, etc. to another," late 14c., proselite, "a convert, especially "a heathen convert to Judaism" (in Biblical writings, e.g. Matthew xxiii.15, Ezekiel xiv.7), from Old French proselite (13c., Modern French prosélyte), from Late Latin proselytus, from Greek prosēlytos "convert (to Judaism), stranger," literally "one who has come over."
It is a noun use of an adjective meaning "having arrived," from pros "from, forth, toward" (see pros-) + eleusomai "to go, come" (from PIE *elu-to-, from root *leudh- "to grow up, come out" (see liberal (adj.)).