Orenga, who took over from Italian Sergio Scariolo in November 2012, was widely blamed for Spain's failure and some of the local fans attending Sunday's final in Madrid, in which United States thrashed Serbia 129-92, chanted for him to go.
"Juan Antonio Orenga has today informed the FEB that he is stepping down as coach of the national team as he believes the expected results at the World Cup have not been achieved and to facilitate future planning in the short and medium term," the FEB said on their website.
"The FEB would like to thank Juan Antonio Orenga for his work and commitment, while at the same time continuing to count on his experience and knowledge - in a post in the technical staff that has yet to be decided - for the development and improvement of our sporting model," they added.
Spain's defeat to France was a huge shock for the home nation, already reeling from the failed title defence of the Spanish football team at the World Cup finals in Brazil.
(Reporting by Iain Rogers, editing by Justin Palmer)
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