A club statement said: "Real Madrid CF. announce that Julen Lopetegui will be the coach of the first team during the next three seasons".
However, Lopetegui's appointment is another surprise from Los Blancos, particularly as he only signed a new deal to remain in charge of Spain until 2020 in May, per BBC Sport.
"Julen Lopetegui will join the club after Spain's participation in the World Cup, after two years leading the national team".
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It will be the first World Cup appearance for the Tottenham striker, and Kane said that he wants to improve his scoring record in the big tournaments.
Lopetegui has never lost a match as Spain coach since taking the reins in July 2016 in the wake of the European Championship, earning 14 wins with six draws for the second-longest unbeaten start by a coach in Spain's history.
Lopetegui is now preparing to lead Spain at the World Cup but the 51-year-old will depart his role as national team coach at the end of the tournament.
Zidane's shock departure came after he had guided Madrid to a third straight Champions League title.
It remains to be seen if he will head to Real as a World Cup victor, though Spain's squad is stocked with exciting talent.
They face a World Cup group containing Iberian rivals Portugal, as well as Morocco and Iran.