Spaniard Benitez, 55, was relieved of his duties following a meeting of the club’s board on Monday.
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.
Benitez’s Real Madrid record
Why sack Benitez?
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.
The right replacement?
For a man with no experience of managing at the top level, Zidane’s appointment could be considered a risk – but he has long been seen as a future Real boss.
Zidane has been coach of the club’s B team – who are second in the Spanish third tier – since 2014. Prior to that he was an integral member of the backroom staff under then Real boss Carlo Ancelotti, who led the team to ‘La Decima’ – the club’s 10th European Cup.
During his playing career, the Frenchman was one of Real’s key ‘Galacticos’ – a label given to the expensive players signed by Perez during his first spell as president in the early to mid-2000s.
In 2001, Real paid Juventus a then world record fee of £45.8m for the midfielder, who had already won the World Cup and European Championship.
At the Bernabeu, he played alongside players such as Luis Figo, Raul and Ronaldo, and also featured in the same midfield as England captain David Beckham.
In the five years before his retirement, he helped Real win the league in 2003 and was named Fifa world player of the year for a third time.
But perhaps his defining moment came during the 2002 Champions League final, when he scored a stunning volley against Bayer Leverkusen at Hampden Park.
Spanish football writer Andy West:
“The first major criticism arrived following a 1-1 draw with local rivals Atletico Madrid in October.
“But that was nothing compared to the avalanche of abuse endured by Benitez after Barcelona’s sensational 4-0 Clasico victory in November, which concluded with loud chants for the former Liverpool manager’s dismissal ringing around the Bernabeu after his team were utterly outclassed by their eternal rivals.
“Benitez survived that trauma, but he never really recovered and from that moment his departure was just a matter of time, with every home game since the defeat by Barca preceded by loud jeers when Benitez’s name was announced with the team line-ups.
“So the news of his departure comes as no surprise, with Benitez’s reign finally buckling under the weight of weeks of relentless pressure. ”
What next for Benitez?
Benitez may be loved in Liverpool and Valencia, but his reputation as a manager has diminished in his past two jobs – at Napoli and Real.
Having won the Champions League at Anfield and the Uefa Cup with Valencia, the Spaniard replaced Walter Mazzarri as Napoli boss in May 2013.
He won the Coppa Italia in his first season, but things soured in his second and final campaign.
Napoli failed to qualify for the Champions League despite the big-money signings of Gonzalo Higuain, Jose Maria Callejon, Raul Albiol and Dries Mertens, with Benitez criticised for his rotation policy and stubborn adherence to a 4-2-3-1 formation.
West Ham co-chairman David Sullivan said last month that Benitez was“two hours away” from being appointed Hammers boss before he took the Real job.
Benitez does have a trophy-laden CV, including the Europa League from his short spell at Chelsea – where he failed to win over fans after replacing the popular Roberto di Matteo – and Club World Cup and Italian Super Cup at Inter Milan.
That may tempt other Premier League clubs to turn to a man whose family home is still in Liverpool.
And what next for Mourinho?
In appointing Zidane, Real overlooked one of their notable former managers.
Jose Mourinho guided the club to the league title in 2012 and – following his sacking by Chelsea last month – is available again.
He has unfinished business at the Bernabeu having failed to win the Champions League – a prize coveted perhaps more than any other by Los Blancos.
But there were reports his relationship with Ronaldo broke down during his last spell in charge, while he also had high-profile clashes with fan favourites Sergio Ramos and Iker Casillas.
Following Mourinho’s departure from Chelsea, Perez said there would be no imminent return to the Bernabeu for the ‘Special One’.
Reaction from the football world
Speaking on BBC Radio 5 live, former Real president Ramon Calderon criticised Perez, who trained as a civic engineer:
“He is an engineer – if you and I were asked to build a bridge, the logical conclusion is that it will fall down.
“He decided to sack Carlo Ancelotti when everyone loved him. I wish Zidane all the best but it will be difficult. If he is not successful, Jose Mourinho will be on the bench in June I am sure.
“Perez didn’t say anything about the change. Why? That is the real story about this club.
“I think the players like Zidane. He won everything with Real Madrid. I am sure the fans will receive him in a very good way.”
Former Real Madrid manager John Toshack on BBC Radio Wales Sport:
“It is 30 years since I first went to Madrid. I remember thinking ‘two years here is enough for anybody’. You have to be winning things and being very successful to stand it.
“The rules are the same. Losing 4-0 at home to Barcelona will have done Rafa an awful lot of damage.
“The president is under pressure and he has taken the easy option.
“Zidane was a terrific player but his managerial experience is zero. It is a last throw of the dice for Florentino Perez. He idolises Zidane and always has done. He is a human shield for the president now. If this one doesn’t come off there will be changes at the top.”
Burnley midfielder Joey Barton on BBC Radio 5 live:
“It is an arms race. A manager who doesn’t win the European Cup is going to be looking over his shoulder. How long can these great clubs keep interchanging parts?
“You forget how deeply political Real Madrid is. It is not just about football. How many clubs of that size would be run by an engineer who runs property?”
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