The Belgian side said on their website they had signed the 43-year-old Garrido until the end of the season, with an option for one further season.
Garrido took charge at Villareal in February 2010 and guided them to fourth place in the Spanish league in 2011.
He left last December after failing to earn a single point in the Champions League and slipping to third from bottom in La Liga.
Bruges sacked previous coach Leekens earlier this month, having only appointed him in May. Leekens abruptly walked out as manager of the Belgian national side to succeed German Christoph Daum at Bruges.
Garrido will arrive at a club still in contention in the Europa League, but with a wretched current league run of five consecutive losses, including last weekend's 6-1 rout at Anderlecht.