early 15c., "to pledge," from Middle French engagier, from Old French en gage "under pledge," from en "make" + gage "pledge," through Frankish from Proto-Germanic *wadiare "pledge" (see wed).
It shows the common evolution of Germanic -w- to French -g-; cf. Guillaume from Wilhelm). Meaning "attract the attention of" is from 1640s; that of "employ" is from 1640s, from notion of "binding as by a pledge." Specific sense of "promise to marry" is 1610s (implied in engaged).