Frenchman Desabre left the club following a string of poor results. He had replaced Zoran Manojlovic in January after the club parted ways with the Serb after just six months.
"I'm very proud to start this new stage with Wydad," the 50-year-old Garrido said in a video published by the Moroccan giants. The length of his contract was not disclosed.
The former Villarreal and Real Betis boss has previously guided both Egyptian heavyweights Al-Ahly and Morocco's Raja Casablanca to the Confederation Cup title.
Garrido was dismissed by Tunisian club Etoile du Sahel at the start of February. He will face his old side on Saturday in the quarter-finals of the CAF Champions League in his first game with Wydad.