He cited Chelsea signing then Italy boss Antonio Conte before Euro 2016 and Manchester United confirming Dutch manager Louis van Gaal's appointment before the 2014 World Cup.
"Fernando Hierro will assume the position of national coach in the World Championship of Russia and will appear before the media accompanied by the president RFEF, Luis Rubiales", a statement from the federation said.
"I know there's going to be criticism whatever I do", said Rubiales.
"I am very calm about everything I have done". He seems a top trainer and that makes it harder to make the decision.
Lopetegui was spectacularly axed on Wednesday after it emerged he had agreed to take charge of Real Madrid after the World Cup.
Rubliales quickly replaced Lopetegui with the director of football, Fernando Hierro.
There were initially reports that the Spain team had tried to fight to keep their manager in place however according to Spanish newspaper SPORT only captain Sergio Ramos spoke up in defence of his soon to be club boss.