During two separate spells, the 52-year-old took charge of 47 matches, boasting a record of 26 wins, 14 draws and seven defeats.
Enrique's exit has come off the back of a disappointing World Cup, with the 2010 champions being eliminated in the last-16 stage of the competition by Morocco.
The former Barcelona head coach only had a contract with Spain until the end of December, and it was announced on Thursday that he would be leaving his role.
La Roja have already confirmed his replacement, with Luis de la Fuente stepping up from his role with Spain Under-21s to become the new head coach.
"I can only be super grateful to those who signed me twice (president Luis Rubiales and sporting director Jose Francisco Molina). To all the employees of the RFEF with whom we share experiences and experiences of all kinds, thank you very much," Enrique wrote on his official Twitter account.
"Of course, to the players who have been exemplary in their behaviour and faithful to the idea that I raised. I'm sorry I couldn't help you more.
"Also, to the assistants, doctors, physios, props, security as well as the team manager Nuria and the nutritionists, who all worked tirelessly to help the players and the staff in everything that we needed. It's been very special to be a part of this.
"Last but not least, to the fans who have uniformly transmitted their support at all times and especially when times have been hardest.
"It's time to say goodbye and in these cases just a little reflection. What the team needs is your SUPPORT in all its meaning so that Luis de la Fuente can achieve everything he proposes. Let's go SPAIN! Farewell. Thank you!"
According to Cadena SER, Enrique had been keen to continue in the role, but RFEF president Rubiales and sporting director Molina decided that a change needed to be made.
The report claims that the former Barcelona head coach had expected to receive a renewal offer.
Spain will next be in action against Norway in March, which will represent their first match in their qualification campaign for Euro 2024.