1640s, "one who calculates, a reckoner, one whose occupation is to make arithmetical calculations," agent noun from compute (v.).
Meaning "calculating machine" (of any type) is from 1897; in modern use, "programmable digital electronic device for performing mathematical or logical operations," 1945 under this name (the thing itself was described by 1937 in a theoretical sense as Turing machine). ENIAC (1946) usually is considered the first.
Computer literacy is recorded from 1970; an attempt to establish computerate (adjective, on model of literate) in this sense in the early 1980s didn't catch on. Computerese "the jargon of programmers" is from 1960, as are computerize and computerization.
WASHINGTON (AP) — A New York Congressman says the use of computers to record personal data on individuals, such as their credit background, "is just frightening to me." [news article, March 17, 1968]
Earlier words for "one who calculates" include computator (c. 1600), from Latin computator; computist (late 14c.) "one skilled in calendrical or chronological reckoning."