The 38-year-old, who previously played at the club and worked as an assistant coach, takes over from Philippe Montanier. He has signed a deal to the end of the 2020-21 campaign, the club said in a brief statement.
Leye, who won three caps for Senegal in 2008, moved from west Africa as a teenager to play in France but spent most of his career in Belgium, eventually retiring two seasons ago.
The former striker was hired to work under Michel Preud’homme at Standard with a view to eventually taking over as coach. However, when Preud’homme left earlier than expected in June, club management hesitated to promote Leye and chose former France under-20 coach Montanier instead.