Middle English scolere, from Old English scolere "student, one who receives instruction in a school, one who learns from a teacher," from Medieval Latin scholaris, "a pupil, scholar," noun use of Late Latin scholaris "of a school," from Latin schola (see school (n.1), and compare scholastic).
The Medieval Latin word was widely borrowed (Old French escoler, French écolier, Old High German scuolari, German Schüler). Not common in English before 14c. and the modern use might be a reborrowing. In British English it typically has been restricted to those who attend a school on a scholarship (1510s).
The spelling in sch- begins to appear late 14c. The broader meaning "learned person," especially one having great knowledge of philosophy and classical literature, is from late 13c.