The club finished second in the Campeonato Brasileiro last season, but have yet to win a game in the 2011 campaign and have picked up just three points from their first five games.
Despite support from the board, Cuca informed Cruzeiro officials of his decision on Sunday morning and leaves after a year in charge.
Santana, who has previously managed South Africa and was most recently with Botafogo, will be officially unveiled as the new coach on Monday.
A statement on Cruzeiro’s official website read: “The coach’s debut will be on Saturday against Coritiba at the Alligator’s Arena in Sete Lagoas in the sixth round of the Brazilian championship.”
Cruzeiro’s final game under Cuca was a 1-1 draw away to America Mineiro on Saturday.
