The Frenchman will replace Santiago Solari, who was in charge for less than five months.
Former Real midfielder Zidane, 46, left in May after leading the club to a third straight Champions League trophy.
Solari is set to be sacked after a 4-1 win over Real Valladolid on Sunday - which followed a shock Champions League exit to Ajax.
That 4-1 home defeat and 5-3 aggregate loss to the Dutch side was the final straw for Real president Florentino Perez.
The defeat by Ajax followed two consecutive defeats by Barcelona in El Clasico - a 1-0 loss in La Liga and a 3-0 thrashing in the Copa del Rey.
Four and a half months later it was Real's turn to fire him.
Reserve-team boss Solari came in as caretaker before being given a contract to 2021 on 13 November. SHARE THIS STORY USING ANY OF THE BUTTON BELOW ⬇ PLACE YOUR TEXT ADVERT BELOW ⬇⬇⬇