The Spanish Football Federation (RFEF) have announced Luis Enrique has left as Spain manager due to personal reasons.
Enrique has been experiencing personal problems in recent months, with his time in charge of La Furia Roja ending after 11 months.
"Luis Enrique has informed us that he will not continue as a selector. I have to thank him," said Rubiales. "We've been united with him. He will always find the RFEF doors open to him.
"The decision of the RFEF is to trust Robert Moreno as a coach. He will remain in charge for the same duration of the contract that was already signed. They will be in charge of taking us to the Euro 2020 and doing a good job if we qualify."
Moreno thanked the RFEF for their trust in him moving forward.
"I want to thank you for the trust you place in us," Moreno said. "It's a bittersweet day.
"I didn't expect to be first coach in this way. We're going to work to finish the top work that Luis started."
Enrique was not present in the dugout for recent matches against Malta, the Faroe Islands and Sweden.
And now a decision to walk away and focus on his private life has been taken, with long-term assistant Moreno stepping up.
Moreno has been Enrique's assistant at Roma, Celta Vigo and Barcelona.
Spain's next fixtures are the Euro 2020 qualifiers in September against Romania and the Faroe Islands.
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