Enrique signed a two-year contract with the national team last week, and will lead La Roja into their qualification campaign for Euro 2020.
Spain incredibly sacked Lopetegui on the eve of the 2018 World Cup due to the manner in which he handled being appointed Real Madrid boss, and it was Hierro that led the nation into this summer's tournament.
Enrique was keen to pay tribute to both Lopetegui and Hierro, while the former Barcelona manager said that he was "very excited for the big challenges that await".
"The aim is to continue the work of Lopetegui and Hierro," Diario Sport quotes Enrique as saying. "We have been analysing everything and we believe the foundations are in place to continue to carry on and re-find success for the team.
"Both men worked extremely hard in their roles and we thank them for everything but football is a continuous cycle and winning trophies is not easy. At Barcelona we had similar ideas of evolution, taking decisions based on ideas of winning more matches and more trophies.
"I know what this job entails, and I am fortunate enough to have the trust of the president, whom I thank, and I hope I can impress in the role. I am very excited for the big challenges that await."
Spain's next match is against England in the UEFA Nations League on September 8.