1843, "compositor," from type (n.) + -ist. Meaning "person who operates a typewriter" is from 1884.
Entries linking to typist
type n.
late 15c., "symbol, emblem," from Latin typus "figure, image, form, kind," from Greek typos "a blow, dent, impression, mark, effect of a blow; figure in relief, image, statue; anything wrought of metal or stone; general form, character; outline, sketch," from root of typtein "to strike, beat," from PIE *tup-, variant of root *(s)teu- (1) "to push, stick, knock, beat" (see steep (adj.)).
Extended 1713 to printing blocks of metal or wood with letters or characters carved on their faces, usually in relief, adapted for use in letterpress printing. The meaning "general form or character of some kind, class" is attested in English by 1843, though the corresponding words had that sense in Latin and Greek. To be (someone's) type "be the sort of person that person is attracted to" is recorded from 1934.
-ist
word-forming element meaning "one who does or makes," also used to indicate adherence to a certain doctrine or custom, from French -iste and directly from Latin -ista (source also of Spanish, Portuguese, Italian -ista), from Greek agent-noun ending -istes, which is from -is-, ending of the stem of verbs in -izein, + agential suffix -tes.
Variant -ister (as in chorister, barrister) is from Old French -istre, on false analogy of ministre. Variant -ista is from Spanish, popularized in American English 1970s by names of Latin-American revolutionary movements.