This isn’t really my area (I am a PhD student, and my research focuses upon the medieval era), but I would say that the answer to your question depends upon which type of well you have in mind.

Dug wells are quite common from the Iron Age onwards with earlier, Neolithic examples occasionally cropping up, e.g. according to a 2009 BBC report (http://news.bbc.co.uk/2/hi/europe/8118318.stm) wells dating from ca. 8500–7000 BCE have been found in Cyprus.

Hand-dug wells lined with wood were created by the Linear Pottery culture in what is now Austria–Germany as early as ca. 5000–5200 BCE (Tegel et al.).

The first artesian well was created by Cartesian monks in Artois, France (whence the name) in 1126 using a percussion drilling technique (Gies & Gies, 112).

I hope that helps.

Gies, Frances, & Joseph Gies. Cathedral, Forge, & Waterwheel: Technology & Invention in the Middle Ages. New York: Harper Collins, 1995.

Tegel, W, R Elburg, D Hakelberg, H Stäuble, & U Büntgen. “Early Neolithic Water Wells Reveal the World’s Oldest Wood Architecture”. PLoS ONE 7.12 (2012): e51374. http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0051374

Edited for formatting