1530s, a kind of document in Scottish law, from French signature (16c.) or directly from Medieval Latin signatura "signature, a rescript," in classical Latin "the matrix of a seal," from signatus, past participle of signare "to mark with a stamp, sign" (see sign (v.)).
Meaning "one's own name written in one's own hand" is from 1570s, replacing sign-manual (early 15c.) in this sense. Musical sense of "signs placed it the beginning of a staff to indicate the key and rhythm" is from 1806. Meaning "a distinguishing mark of any kind" is from 1620s.