Leonardo is the latest in a string of storms to affect Spain and Portugal this year. Severe weather had already killed five people and injured hundreds in Portugal last week.
Floods brought by Storm Leonardo battered the Iberian peninsula on Wednesday, forcing thousands of evacuation, shutting schools and cancelling trains.
In Portugal, a man in his 60s was killed after being swept away by the current while attempting to drive across an area flooded by Storm Leonardo in southeastern Portugal, the national civil protection authority reported.
"A vehicle was found with one occupant, so there is one death," the spokesman said, adding that the death took place near a dam in the municipality of Serpa.
In Spain, weather agency AEMET placed parts of the southern region of Andalusia under the highest red alert due to the "extraordinary" rain, warning of floods and landslides.
Andalusia's top emergency official, Antonio Sanz, told a press conference that the situation was "very worrying" in the nearby mountainous municipality of Grazalema.
Grazalema soaked in more than 40 centimetres of rain in just 24 hours, "the usual amount of rainfall in Madrid in an entire year", according to AEMET spokesman Ruben del Campo.
Around 3,500 people had been evacuated in Andalusia, and hundreds of soldiers had been deployed to assist rescue services. All Andalusian schools were closed apart from in the region's easternmost province of Almeria.
Almost all suburban, regional and long-distance trains were cancelled across Andalusia, with no bus replacement services possible due to the state of the roads, dozens of which were closed.
Portugal still reeling from Storm Kristin
Leonardo brought added difficulties for Portugal, already reeling from last week's Storm Kristin, which killed at least five people, injured hundreds and cut off tens of thousands of customers from the power grid.
The emergency services had dealt with more than 3,300 incidents since Sunday, mostly due to flooding, falling trees and landslides, according to the Civil Protection authority.
The service had deployed more than 11,000 people, and around 200 residents were evacuated in central Portugal on Wednesday.
In Alcácer do Sal, south of Lisbon, the Sado river had burst its banks and the rising water had submerged the town's main avenue.
Speaking to journalists on Wednesday afternoon, the Minister for the Environment, Maria da Graça Carvalho, said there is great concern about the consequences of the storm on Thursday, when there will be a "peak" situation.
"According to IPMA forecasts," she said, there will be a further worsening of the weather "on Saturday and Sunday", although it is expected to be "very mild". Carvalho also announced that there would then be "a new peak" of bad weather, "on Monday, Tuesday or Wednesday, at the beginning of next week".
The Lisbon region and the Algarve in the south were most affected, with rain and wind predicted to reach their peak intensity overnight Wednesday to Thursday.