Artell left the Butcher's Arms on Monday to succeed the sacked Steve Davis at Gresty Road, less than two months after joining the Bloods from Welsh Premier League side Port Talbot Town.
Gibraltar international Artell, 36, scored 6 goals for Crewe in eighty-two appearances. The former Port Vale and Northampton defender's final act as a player was to hold aloft the League Two Play-Off Trophy at Wembley in 2012 after skippering the side to promotion before returning to the club in July 2014 as academy operations manager.
Droylsden secretary Bryan Pace said: "Our centre-half has left us to be first-team manager at Crewe, he was the academy manager but after they sacked Steve Davis he was offered the position which is a great opportunity for him. Congratulations to David, his stay at the Bloods was brief and everyone at the club wishes him well."
Davis, who was the fourth longest-serving boss in the country after succeeding Dario Gradi in 2011, was sacked after more than five years at the helm at Gresty Road.