Lopetegui will take over Zidane's duties after the World Cup.
Lopetegui and the Spain squad are now at their training base in the southern Russian city of Krasnodar.
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Spain are among the favourites to win the World Cup after an nearly flawless qualifying campaign, and he will be hoping that the announcement does not overly unsettle his squad just before the competition gets under way.
In a brief statement to announce the appointment, the Madrid giants said Lopetegui had been appointed on a three-year contract.
Zidane's resignation came as a big shock, as he had just led Real Madrid to a third consecutive UEFA Champions League triumph.
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He thanked the pope for his concern for the common good and said he prayed "that one day all the truth will shine". Since 2000, about 80 Roman Catholic priests have been reported to authorities in Chile for alleged sexual abuse.
"My future? The important thing is the World Cup and not to think of anything else that can divert you or upset you", De Gea, who is on national team duties with Spain told reporters. Tottenham Hotspur manager Mauricio Pochettino had initially emerged as the leading candidate to replace the Frenchman. He played briefly for both Real Madrid and their rivals Barcelona, amd managed the Madrid B team.
The 51-year-old took up his current job two years ago and is yet to lose a game, clocking up 14 wins and six draws from his 20 matches in the helm of La Roja.
He coached Madrid's feeder club Castilla in 2008/09 before taking charge of Spain's youth teams.
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He previously had a spell as manager of Porto, as well as with the Spanish national youth team set-up and at Real's B team. The 51-year-old was a goalkeeper in his playing days, and played for both Madrid and Barcelona during his career.
In May, he signed a two-year extension to remain as Spain coach until 2020 but the call of Madrid has proved stronger.