early 15c., "to pledge" (something, as security for payment), from Old French engagier "bind (by promise or oath), pledge; pawn" (12c.), from phrase en gage "under pledge," from en "in" (see en- (1)) + gage "pledge," through Frankish from Proto-Germanic *wadiare "pledge" (see wed). It shows the common evolution of Germanic -w- to central French -g- (see gu-).
Meaning "attract and occupy the attention of" is from 1640s; that of "employ, secure for aid, employment or use" is from 1640s, from notion of "binding as by a pledge;" meaning "enter into combat or contest with" is from 1640s. Specific sense of "promise to marry" is 1610s (implied in engaged). Machinery sense is from 1884. Also from the French word are German engagiren, Dutch engageren, Danish engagere.