1580s, "handy, dexterous, having special manual ability," apparently from East Anglian dialectal cliver "expert at seizing," perhaps from East Frisian klüfer "skillful," or Norwegian dialectic klover "ready, skillful," and perhaps influenced by Old English clifer "claw, hand" (early usages seem to refer to dexterity). Or perhaps akin to Old Norse kleyfr "easy to split," from Proto-Germanic *klaubri‑ from PIE root *gleubh- "to tear apart, cleave." Extension to intellect is first recorded 1704.
This is a low word, scarcely ever used but in burlesque or conversation; and applied to any thing a man likes, without a settled meaning. [Johnson, 1755]
The meaning has narrowed since, but clever also often in old use and dialect meant "well-shaped, attractive-looking" and in late 18c. and 19c. American English sometimes "good-natured, agreeable." Related: Cleverly; cleverness.