The French right-back becomes Crewe's second signing of the summer following the arrival of the Lincoln forward Vadaine Oliver earlier this month.
The 26-year-old has put pen to paper on a two-year deal with the option of another 12 months.
Audel began his career in his homeland as a junior with his hometown club Nice and later went on to play for FC Istres and Auxerre before moving to Italy where he had spells with Triestina, San Marino (on loan) and AC Pisa.
He also had a short stint with Slovenian club MNK Izola before moving to Macclesfield in January 2013.
Audel, who has also operated as a centre-back during his career, made 20 appearances for the Silkmen last season, scoring his only senior goal in a 2-1 win over Alfreton in February.