Middle English shiften, from Old English sciftan, scyftan "arrange, place, put in order" (a sense now obsolete), also "divide, separate, partition; distribute, allot, share" (now obsolete or provincial), from Proto-Germanic *skiftan (source also of Old Norse skipta "to divide, change, separate," Old Frisian skifta "to decide, determine, test," Dutch schiften "to divide, turn," German schichten "to classify," Schicht "shift"). This is said to be related to the source of Old English sceadan "divide, separate" (see shed (v.)).
By c. 1200 as "to dispose; make ready; set in order, control," also intransitive, "take care of oneself." Thus "manage to succeed, make out a livelihood" (as in shift for oneself, 1510s; also compare makeshift).
The sense of "to alter, to change" appeared by mid-13c. (compare shiftless). Also from mid-13c. in the transitive sense of "remove and replace with another or others," originally especially of clothing, hence "put on and replace one's clothes" (c.1400).
From c. 1300 as "to go, move, depart; move (someone or something), transport" as from one place or position to another. The meaning "change the gear setting of an engine" is from 1910; to shift gears in the figurative sense is from 1961. Related: Shifted; shifting.