c. 1300, porche, "covered entrance; roofed structure, usually open on the front and sides, before an entrance to a building," from Old French porche "porch, vestibule," from Latin porticus "covered gallery, covered walk between columns, arcade, portico, porch," from porta "city gate, gate; door, entrance," from PIE root *per- (2) "to lead, pass over."
The Latin word was borrowed directly into Old English as portic. Especially (late 14c.) "a covered walk or colonnade on the front or side of a building." In U.S., used by 1832 for what the British call a veranda.