The 48-year-old has become La Roja's new coach following caretaker boss Fernando Hierro's decision to stand down from the position on the back of a disappointing World Cup.
Spain were beaten by tournament hosts Russia on penalties in the last 16 following a 1-1 draw at the Luzhniki Stadium in Moscow.
The 2010 winners were touted as one of the pre-tournament favourites but their chances were heavily disrupted by the decision to sack manager Julen Lopetegui on the eve of the competition.
Lopetegui was named as Zinedine Zidane's successor at Real Madrid, with the Spanish Football Federation angered by the timing of the announcement with the World Cup just around the corner.
But now Spain have turned to Luis Enrique to guide the national team ahead of the 2020 European Championship.
Speaking at a press conference that was not attended by the new coach, Spanish FA chief Luis Rubiales said: "The decision has been unanimous. This selection complies with all parameters from the sports management criteria.
"Luis Enrique comes with his staff, but he will talk about that next week."
Luis Enrique takes over from Hierro in what will be his first managerial role since leaving Barcelona in 2017.
Luis Enrique also made 12 appearances for Spain as a player.