Anderlecht made the announcement on Saturday, saying that the 45-year-old Welshman had signed a contract until 2022 to join "TeamKompany".
Kompany has become Anderlecht's player-manager after helping Manchester City to become the first team to win the English domestic treble.
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Former Manchester United and Chester City midfielder Davies has worked for Manchester City for nine years, succeeding Patrick Vieira as head of the club's elite development squad, including the under-23 side.
"When Vinny asked me to make the move with him to RSC Anderlecht, I didn't hesitate," Davies said in a statement released by the Belgian club.
"We are starting a beautiful project: taking RSC Anderlecht back to the place where they belong, with special emphasis on the development of talented young players."
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