At Language Log, in the post Giveth and taketh, Arnold Zwicky mentions current "snowclones" such as "Globalization giveth ... Globalization now taketh away" modelled on the well-known "The Lord giveth, and the Lord taketh away". He also notes, with reference to Michael Macrone's Brush Up Your Bible, how this isn't actually in the Bible, but is a misquotation (or paraphrase) of Job 1: 20-21 in the 1611 King James Version.
Then Job arose, and rent his mantle, and shaved his head, and fell down upon the ground, and worshipped,
And said, Naked came I out of my mother's womb, and naked shall I return thither: the Lord gave, and the Lord hath taken away; blessed be the name of the Lord.
But when did it arise? This is a nice example of how it's possible to do a historical search with Google Books, using the following syntax to specify date range (e.g. "Lord giveth" "Lord taketh away" date:1700-1835).
This finds plenty of hits showing the long history. It turns up in a number of late 18th and early 19th century novels, such as John Galt's 1822 The Provost (here), the anonymous 1805 Belville-House (here), Mary Meeke's 1799 Ellesmere (here), and Horace Walpole's 1764 gothic novel The Castle of Otranto (here). The oldest direct uses in relation to Job I can find in general prose accounts are in the 1718 A Faithful Register of the Late Rebellion (here) and the 1714 The History of the Life of Thomas Ellwood (here). Older still is Thomas Marbury's 1650 A Commentarie Or Exposition Upon the Prophecie of Habakkuk: Together with Many Usefull and Very Seasonable Observations. While it doesn't feature the full quotation, it nevertheless uses the "Lord giveth ... Lord taketh away" construct (here). At this point, you need to start considering archaic spellings. To cut to the chase, as probably anyone more Christian could have done long since, it tracks down to the 1549 Book of Common Prayer, in The Ordre for the Buriall of the Dead:
WE brought nothyng into this worlde, neyther may we carye any thyng out of this worlde. The Lord geveth, and the Lord taketh awaie. Even as it pleaseth the Lorde, so cummeth thynges to passe: blessed be the name of the Lorde.
This, the first English prayer book, is probably the main source. Who actually coined the paraphrase of Job is uncertain. As the Society of Archbishop Justus website says, Thomas Cranmer is assumed to be the main author, but as the work was done by committee and no records of the editorial process exist, we can't be sure. However, Michael Macrone is definitely off the mark with his "nice try with the Renaissance conjugations". It's not a "nice try"; it was coined when they were current. It took me a while to get there, not being religious, but it's surprising that the author of Brush Up Your Bible didn't spot it.
The "-eth" ending, by the way, is a Middle English and early Modern English construct that rapidly fizzled out in Modern English post-1600 except when people wanted a religious or poetic tone (see Early Modern English, Charles Laurence Barber, Edinburgh University Press, 1997, ISBN 0748608354, p.166 onward, for a good account of the decline of "-eth"). However, Bible translations of the 1500s-1600s - notably the KJV - tended to incorporate archaicisms of language that were already declining (in the KJV's case, partly because it drew on earlier translations, partly because of the perceived formal tone of "-eth"). Even so, "Lord giveth ... Lord taketh away" isn't in any of them, nor in the older Wyclif translation.
The strong factor for its survival over 500+ years appears to be its incorporation as a linguistic fossil in the standard Christian committal and burial service derived from the Book of Common Prayer. This seems a more likely reason for its continuing currency than it being, as Professor Zwicky suggests, a popular misquotation persisting because people see it as an "improvement" on the original wording of Job.
All that said, I think it is an improvement, in the sense of it being an inspired decision to introduce parallelism, which created a powerful and lasting epigram.