The Turle Knot is a popular knot for connecting a fly with a turned up or turned down eye to a line. There are several variations to this knot and this one would be considered the “Improved Turle Knot”. 

Run the line through the eye of the hook, then tie a loose double overhand knot in the end of the line.

Pass the open loop over the hook and tighten the whole thing so that the loop tightens around the eye.