The club from Belo Horizonte have not won any of their five matches, including Saturday's 1-1 draw with city rivals America-MG, in the championship having finished runners-up last year under Cuca.
Cruzeiro said Cuca, who had taken charge a year ago, handed in his resignation on Sunday morning despite the club's wish for him to stay on.
Santana, who quit Botafogo in March after 14 months with the Rio team, will be officially unveiled as Cruzeiro coach on Monday, they said on their website.
"The coach's debut will be on Saturday against Coritiba at the Aligator's Arena in Sete Lagoas in the sixth round of the Brazilian championship," Cruzeiro added.
The experienced 62-year-old Santana coached South Africa in 2008 and 2009 but was sacked nine months before the country hosted last year's World Cup.
Sao Paulo remained top of the standings on a maximum 15 points with a 2-0 away win over Ceara after captain Rogerio Ceni saved a penalty and 19-year-old Brazil midfielder Lucas scored a superb goal.
Ceni's penalty save from Osvaldo midway through the first half ended Ceara's dominance and Marlos opened Sao Paulo's account before halftime.
Lucas, in his last match before leaving for Argentina with the Brazil squad for next month's Copa America, dribbled past Ceara Fernando Henrique in the 67th for the second goal.
Sao Paulo's fine start to the championship will be put to the test in the coming weeks while they are deprived of Lucas until late July and four young players picked by Brazil for the Under-20 World Cup in Colombia from July 29 to Aug. 20.
Luiz Felipe Scolari's Palmeiras are four points behind after a 5-0 rout of Avai with strikers Kleber and Luan scoring twice each.
Flamengo, with an uninspired Ronaldinho who came off to boos during the second half, held on for a 0-0 draw with Botafogo despite playing with 10 men for more than an hour after Argentine midfielder Dario Bottinelli earned a second booking for diving in the box.
Champions Fluminense lost their second consecutive match under new coach Abel Braga, a 1-0 upset at home to promoted Bahia on Saturday. Fluminense have six points from two wins.
