Enrique has left his role with the national side following the team's disappointing 2022 World Cup, which saw them lose on penalties to Morocco in the last-16 stage of the competition.
"The sports management of the RFEF has transferred to the president a report in which it is determined that a new project should start for the Spanish Soccer Team, with the aim of continuing with the growth achieved in recent years thanks to the work carried out by Luis Enrique and their collaborators," read a statement from the Royal Spanish Football Federation.
"Both the president, Luis Rubiales, and the sports director, Jose Francisco Molina, have transmitted the decision to the coach.
"The Asturian coach managed to give a new impetus to the national team since his arrival, in 2018, through a profound renovation that has consolidated a generational change in the team and in Spanish football.
"The RFEF energetically wishes Luis Enrique and his team the best of luck in their future professional projects. The coach earns the love and admiration of his collaborators in the national team and of the entire Federation, which will always be his home."
The Spanish FA have now announced Enrique's replacement, with De la Fuente named as the new head coach.
"The RFEF [Royal Spanish Football Federation] has chosen Luis de la Fuente as the new absolute national coach," read the statement.
"The sports director, Jose Francisco Molina, has forwarded a report to the president, Luis Rubiales, in which he recommends the choice of the coach from La Rioja, until now the U-21 coach, to lead the new stage that begins after the World Cup in Qatar."
De la Fuente became manager of Spain Under-19s in 2013, while he has spent the last four years with Spain Under-21s.
The 61-year-old has won the European Championship with both Spain Under-19s and Spain Under-21s, while he delivered a silver meal at the 2020 Olympics with Spain Under-23s.
As a player, he turned out for Athletic Bilbao, Sevilla and Alaves, ultimately retiring in 1994, while he made nine appearances at youth level for Spain during his professional career.
La Roja's next competitive match is against Norway on March 23, with the team set to begin their qualification campaign for Euro 2024.
The 2010 world champions will also take on Scotland, Georgia, Cyprus in Group A, with the tournament set to take place in Germany following the completion of the 2023-24 campaign.