late 14c., "government, rule, authority, control," a sense now obsolete, from Old French regiment "government, rule" (14c.), from Late Latin regimentum "rule, direction," from Latin regere "to rule, to direct, keep straight, guide" (from PIE root *reg- "move in a straight line," with derivatives meaning "to direct in a straight line," thus "to lead, rule").
The military meaning "unit of an army" is recorded by 1570s, from a sense in French; the reference in the word originally was to permanent organization and discipline. The exact number of soldiers in a regiment has varied widely over time and place.
