1841, from train (v.) in the "instruct" sense + -ee.
Entries linking to trainee
train v.
"to discipline, teach, bring to a desired state by means of instruction," 1540s, probably from earlier sense of "draw out and manipulate in order to bring to a desired form" (late 14c.), specifically of the growth of branches, vines, etc. from mid-15c.; from train (n.). Sense of "point or aim" (a firearm, etc.) is from 1841. Sense of "fit oneself for a performance by a regimen or exercise" is from 1832. The meaning "to travel by railway" is recorded from 1856. Related: Trained; training.
-ee
word-forming element in legal English (and in imitation of it), representing the Anglo-French -é ending of past participles used as nouns (compare -y (3)). As these sometimes were coupled with agent nouns in -or, the two suffixes came to be used as a pair to denote the initiator and the recipient of an action.
Not to be confused with the French -ée that is a feminine noun ending (as in fiancée), which is from Latin -ata.