"Without a doubt, I have no intention to remain as coach, but you have to be discreet. No matter what the result of the Euros, I had no doubt about what my future would be," he told Spanish public radio RNE, confirming reports in sports dailies AS and Marca that he had quit.
Spain were eliminated from Euro 2016 on Monday following a meek 2-0 defeat to Italy and Marca says that ex-Granada coach Joaquin Caparros will take over.
Del Bosque, 65, who succeeded the late Luis Aragones after Spain's triumph at Euro 2008, is a popular figure in Spain after leading the national team to a maiden World Cup victory in 2010 and a second consecutive European Championship two years later.
But some felt a fresh start was needed after Spain's failure to advance beyond the group stage at the 2014 World Cup finals in Brazil, however del Bosque had stayed in the job for France.
He said he will remain in the post until his contract expired on July 31st. Nobody at the Spanish football federation had asked for his advice regarding who should replace him, he said.
"I would be excited to manage the national team, any Spanish coach would be honoured to take this job. But I hope Vicente stays, he is the best coach possible," Caparros told Marca.
Caparros has managed a host of Spanish clubs including Villarreal, Sevilla, Athletic Bilbao and Levante, but he is currently out of work.
Among the other names tipped to replace del Bosque is former Spain under-21 boss Julen Lopetegui, Granada coach Paco Jemez and former Marseille coach Jose Miguel Gonzalez.