An Etymological Dictionary of the German Language/Gruß
Gruß, m., ‘greeting, salute,’ from the equiv. MidHG. and OHG. gruoȥ, m.; corresponding to Du. groet. ‘To this is allied grüßen, from MidHG. grüeȥen (grüetzen), OHG. gruoȥȥen (gruozzen), wk. vb., ‘to address, accost’ (also with hostile intent ‘to attack’); corresponding to AS. grêtan, E. to greet, Du. groeten, OSax. grôtian, ‘to address,’ OIc. grœta. The latter is probably the primary meaning of the cognates, which are merely West Teut. Origin obscure.