Old English spannan "to join, link, clasp, fasten, bind, connect; stretch, span," from Proto-Germanic *spannan (source also of Old Norse spenna, Old Frisian spanna, Middle Dutch spannen, Dutch spannan "stretch, bend, hoist, hitch," Old High German spannan, German spannen "to join, fasten, extend, connect"), from PIE root *(s)pen- "to draw, stretch, spin" (source also of spin (v.)).
The meaning "to encircle with the hand(s)" is from 1781; in the sense of "to form an arch over (something)" it is first recorded 1630s. Related: Spanned; spanning.