"agile, light and quick in motion, light-footed," c. 1300, nemel, from Old English næmel "quick to grasp, quick at taking" (attested but once), related to niman "to take," from Proto-Germanic *nemanan (source also of Old Saxon, Old Dutch, Gothic niman, Old Norse nema, Old Frisian nima, German nehmen "to take"), perhaps from PIE root *nem- "assign, allot; take."
With unetymological -b- attested from c. 1500 (compare limb (n.1)). Nimble-fingered is from 1620s; nimble-footed from 1590s; nimble-witted from 1610s. Related: Nimbleness. In 17c., English had nimblechaps "talkative fellow."