Zinedine Zidane said he is "very happy to be home" after returning as Real Madrid manager just 10 months after leaving the Spanish giants.
The Frenchman replaces Santiago Solari, who was sacked after less than five months in charge.
Former Real midfielder Zidane, 46, who left in May after leading the club to a third straight Champions League trophy, has agreed to take over until 2022.
Real are currently third in La Liga, 12 points behind leaders Barcelona.
"The best manager in the world has rejoined the club," Real president Florentino Perez said.