early 15c., "person holding a church position," from Medieval Latin incumbentem (nominative incumbens) "holder of a church position," noun use of present participle of incumbere "to obtain or possess," from Latin incumbere "recline on," figuratively "apply oneself to," from in- "on" (see in-(2)) + -cumbere "lie down," related to cubare "to lie" (see cubicle). Extended to holders of any office from 1670s.

1560s, in relation to duties or obligations, from Latin incumbentem (nominative incumbens), present participle of incumbere (see incumbent, n.). The literal, physical sense is rare in English and first attested 1620s.