Enrique has been in charge of Spain less than a year.
Luis Enrique has informed us he will not continue as coach.
We completely respect his situation and continue to do so in the same way. I have to thank him, he has behaved with the RFEF in a "10" manner, we do not have the slightest rebuke.
Rubiales officially presented Luis Enrique, who signed a two-year contract and announced radical changes with regard to call-ups.
Moreno said: "I want to thank you [the RFEF] for placing your trust in us".
The 41-year-old Moreno, who holds a university degree in commerce and worldwide relations, was practically unknown in Spain until he had to fill in for Luis Enrique.
Luis Enrique abandoned the Spain get-together prior to their game against Malta on 26 March, having been on the bench for the meeting with Norway, hurriedly leaving the squad and returning home to Barcelona.
The RFEF had expressed last month their "total commitment" to Enrique and hoped to have him for "many years in charge". The new boss of La Roja said he is grateful for the federation's confidence in him, but also recognised that it was not an easy day.
Spain's next fixtures are the Euro 2020 qualifiers in September against Romania and the Faroe Islands.
After crashing out to Russian Federation in the last 16 of the World Cup, Luis Enrique oversaw impressive wins over England and Croatia in the Nations League, and a 4-1 thrashing of Wales in a friendly.
"It's bittersweet; more sour than sweet", said Moreno. "I always thought about being the head coach but never under these circumstances".