Bulgarian Stoichkov has signed a two-year deal at the Pretoria-based club, whose billionaire mining magnate owner Patrice Motsepe went through three coaches last season.
Stoichkov followed former France manager Henri Michel into the hot seat. Michel spent six months with the Sundowns last season but was fired after they failed to climb the South African Premier League standings.
The 43-year-old Stoichkov was named Europe’s best player in 1994 when he was a prolific striker with Spanish giants Barcelona.
But his coaching career has not been successful with a three-year spell in charge of Bulgaria culminating in failure to reach the 2006 World Cup.
He left Spanish club Celta Vigo just months after taking the job.