"engineer who designs and builds mills and their machinery," late 15c., from mill (n.1) + wright.
Entries linking to millwright
mill n.1
Middle English mille, "building fitted to grind grain," Old English mylen "a mill" (10c.), an early Germanic borrowing from Late Latin molina, molinum "mill" (source of French moulin, Spanish molino), originally fem. and neuter of molinus "pertaining to a mill," from Latin mola "mill, millstone," related to molere "to grind," from PIE root *mele- "to crush, grind." The -n- gradually was lost in English but survives in the surname Milner. Also from Late Latin molina, directly or indirectly, are German Mühle, Old Saxon mulin, Old Norse mylna, Danish mølle, Old Church Slavonic mulinu.
The meaning "mechanical device for grinding grain for food" is from 1550s. The broader sense of "machine for grinding or pulverizing any solid substance" is attested from 1670s. Other types of manufacturing machines driven by wind or water, that transform raw material by a process other than grinding began to be called mills by early 15c. Sense of "large building fitted with machinery for manufacturing" is from c. 1500. In old slang also "a typewriter" (1913); "a boxing match or other pugilistic bout" (1819).
wright n.
Old English wryhta, wrihta (Northumbrian wyrchta, Kentish werhta) "worker," variant of earlier wyhrta "maker," from wyrcan "to work" (see work (v.)). Now usually in combinations (wheelwright, playwright, etc.) or as a surname. A common West Germanic word; cognate with Old Saxon wurhito, Old Frisian wrichta, Old High German wurhto.
The metathesis of an -r- and a vowel in words from Old English also can be seen in thrash, thresh, third, thirty, bird, wrought, and nostril.
Smith was the general term for a worker in metals, and wright for one who worked in wood, and other materials. Hence, in the later English period, smith (which, in Anglo-Saxon, when used without any characteristic addition, was understood as applying more particularly to the worker in iron,) became the particular name of a blacksmith, and wright of a carpenter, as it is still in Scotland. [Thomas Wright, "Anglo-Saxon and Old English Vocabularies," 1884]