Lopetegui will join the club after Spain's participation in the World Cup, after two years leading the national team, according to Real Madrid's website.
Zinedine Zidane left Real Madrid as head coach after winning three consecutive UEFA Champions League titles.
"Lopetegui will join the club once his involvement with the Spanish national squad in the World Cup finals is over, having spent two years in charge of the national side," Real Madrid said, adding that he would sign for the next three seasons initially.
Former goalkeeper Lopetegui, 51, who had spells at Madrid as a player in the late 1980s and managed its B team a decade ago, has been boss of Spain's national side since 2016, in which time he has gone unbeaten, reports Efe.
Rumours as to who might take over at Los Blancos had filled the sporting press in the wake of Zidane's sudden departure at the end of May.
The Frenchman took his leave after winning three consecutive Champions League trophies, saying it was the right time to go.
Lopetegui had on May 22 renewed his contract as Spain coach until 2020.
The news that Zidane's spot on the bench of the Santiago Bernabeu had been filled came just three days before Lopetegui leads Spain's international line-up into its opening Group match against Portugal in Sochi, where the soon-to-be Madrid boss will come face-to-face with one of his future star players, Cristiano Ronaldo.
Spain will later have to overcome Iran and Morocco to advance beyond the group stages.
The line-up, which features the likes of Diego Costa, Sergio Ramos, Andres Iniesta and Gerard Pique, is one of the hot favourites to walk away with the trophy at the end of the campaign in Russia.
(This story has not been edited by Social News XYZ staff and is auto-generated from a syndicated feed.)
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