mid-12c., possibly from Old Danish døja or Old Norse deyja "to die, pass away," both from Proto-Germanic *dawjanan (cf. Old Frisian deja "to kill," Old Saxon doian, Old High German touwen, Gothic diwans "mortal"), from PIE root *dheu- (3) "to pass away, become senseless" (cf. Old Irish dith "end, death," Old Church Slavonic daviti, Russian davit' "to choke, suffer").
It has been speculated that Old English had *diegan, from the same source, but it is not in any of the surviving texts and the preferred words were steorfan (see starve), sweltan (see swelter), wesan dead, also forðgan and other euphemisms.
Languages usually don't borrow words from abroad for central life experiences, but "die" words are an exception, because they are often hidden or changed euphemistically out of superstitious dread. A Dutch euphemism translates as "to give the pipe to Maarten." Regularly spelled dege through 15c., and still pronounced "dee" by some in Lancashire and Scotland. Used figuratively (of sounds, etc.) from 1580s. Related: Died; dies.