According to the OED a similar word also existed in Old English.

I have heard it said that when Scandinavian people (Vikings or Danes) were settling in Britain their language and that of the Angles were mutually intellible to a limited extent. The particular word "reek" could have come from either or both. In Scots it has kept its old meaning of "smoke", which it seems to have lost in standard English where it only has the meaning "smell" or "stench".