Old English rec (Anglian), riec (West Saxon), "smoke from burning material," probably from a Scandinavian source such as Old Norse reykr, Danish rǿg, Swedish rök "smoke, steam," from Proto-Germanic *raukiz (source also of Old Frisian rek, Middle Dutch rooc, Old High German rouh, German Rauch "smoke, steam"), from PIE *reug- "to vomit, belch;" also "smoke, cloud." Sense of "stench" is attested 1650s, via the notion of "that which rises" (compare reek (v.)).
Old English recan (Anglian), reocan (West Saxon) "emit smoke," from Proto-Germanic *reukan (source also of Old Frisian reka "smoke," Middle Dutch roken, Dutch rieken "to smoke," Old High German riohhan "to smoke, steam," German rauchen "to smoke," riechen "to smell").
Originally a strong verb, with past tense reac, past participle gereocen, but occasionally showing weak conjugation in Old English. Meaning "to emit a bad smell" is recorded from 1710 via sense "be heated and perspiring" (early 15c.). Related: Reeked; reeking.