In a statement, officials said seven of the victims were from the United Kingdom, three from Belgium, one from France and another from the United States, as cited by AFP and local media.
The last victim was a Spanish citizen.
“The 13 people who died are eight women and five men, all adults,” the public body responsible for identifying the victims added.
Among the British nationals who died were couple Pete and Fran Gillam, who lived in Bédar, the village that bore the brunt of the wildfires. Their deaths were confirmed by their family.
Posting on Facebook, their daughter Danielle Gillam-Kirton, from Sheffield, said the family were “heartbroken to share that we have received confirmation from the police that Mum and Dad did not survive the fire”.
Nearly 1,500 people were evacuated from Almería province as firefighters battled the flames.
British man Malcolm Timbrell, 70, who lives in the village of Bédar and survived the fires, spoke to the outside his destroyed home high on the hillside.
His wife and friends are believed to be among those killed during the wildfires.
Timbrell described the moment he was separated from the group, and attempted to take refuge in some abandoned cars: “Of the six cars, four of them instantly combusted and as each one started to go, I moved back one car.
“For some reason of fate, the last two cars, although very, very badly singed and paint bubbled and burnt, survived.
“And I survived inside the last one with a cat.”
Spain has suffered frequent and severe heatwaves in recent years, with temperatures often exceeding 40C.
The fire, which has now been contained, burned through about 7,000 hectares (17,300 acres) of land, authorities said.