Real B team coach Zidane, 43, has been promoted to first-team boss.
The Frenchman, a former Real player and World Cup winner, said: "I am going to put my heart and soul into this job so that everything works out well."
Benitez's final game was Sunday's 2-2 draw with Valencia, which left them third in La Liga, four points behind leaders Atletico Madrid.
Zidane is the 11th coach to be appointed in Florentino Perez's 12 years as club president across two spells. The length of his contract has not been made public.
His first match in charge will be Saturday's home La Liga game against Deportivo la Coruna.
Perez is yet to explain why the board of directors took the "difficult" decision to dismiss Benitez, who once coached the club's youth teams.
Speaking at a news conference on Monday, he said: "Let me make clear that this is a great professional and a great person.
"I want to acknowledge the dedication of Benitez during his time as coach of Real Madrid."
Benitez lost only three of his 25 games in charge of Los Blancos and also took them into the last 16 of the Champions League with two games to spare.
An 8-0 home win over Malmo and a 10-2 victory against nine-man Rayo Vallecano - the first time
Real had reached double figures since 1960 - were amongst his most notable successes, but it would seem a combination of factors both on and off the pitch led to his downfall.
One was the 4-0 home defeat by Barcelona in the first El Clasico of the season in November. His defensive tactics were also criticised, while there were reports of a rift with star forward Cristiano Ronaldo.