The body of the climber from Barcelona was found at the foot of the south-facing slope of the "Barre des Ecrins", in Massif des Écrins mountain range in France, Spain's ABC newspaper reported.
The 35-year-old died after falling in a zone with drops as great as 1,100 metres (3,600 feet), said French rescue workers working out of Briançon.
Local authorities have ruled out a judicial investigation into the incident after ruling the death accidental.
The climber set out alone on Sunday along the famous Pré de Madame Carle but was not reporting until fellow campers raised the alarm.
His body has not yet been returned to Spain, French authorities said.
Another Barcelona man also died while climbing on the Massif des Écrins in June.
El cuerpo fue encontrado ayer a los pies de la vertiente sur de la "Barre des Ecrins", dentro de la ruta que el alpinista tenía prevista.