The pair, a woman aged 46 and a man of 61, had been missing for a week after they failed to return to their accommodation.
They were found by chance by a group of hikers at around 1pm on Wednesday on a steep section of the Torre de Altaiz mountain after apparently having fallen to their deaths.
They probably died after falling from "a considerable height" of around 130 metres, said Spanish paper El Comercio, since the bodies were in poor condition when they were found.
Rescue workers took four hours to retrieve the bodies, which were taken to Santander to be identified.
The hikers were last seen by a taxi driver who took them to the bottom of the Fuente Dé cable car.
He told Spanish media that they were dressed in light clothing and were not suitably equipped for mountaineering.
The two Swiss were reported missing last Friday after they failed to return to their booked accommodation, and a formal search was carried out until being called off on Monday.