Although this type of active low pressure system is fairly common in winter, BBC meteorologist Alex Deakin says Saturday's storm has been described as the most damaging since that of December 1999, which killed 88 people and uprooted millions of trees.
The storm tracked south-eastwards and cleared the south-east coast of France during Saturday evening.
The Mediterranean islands of Corsica, Sardinia and Sicily have also been affected.
The sports hall partially collapsed in the town of Sant Boi de Llobregat, Catalonia, with between 20 and 30 youngsters inside, officials said.
The youngsters had gathered to play baseball but the fierce winds drove them to take shelter in a small covered area for spectators, made of concrete, with a corrugated iron roof.
"It seems that the roof shifted and brought down part of the wall," a regional government spokeswoman said.
Local people and fire-fighters helped free the survivors from the rubble but three children aged between nine and 12 died at the scene, and a fourth child died later in hospital. More than a dozen others received treatment for injures.
In other incidents:
In the Landes region of south-western France, near Bordeaux, a driver was killed by a falling tree, a 78-year-old man was killed by flying debris and a third man, 75, was crushed by a tree
A woman, 73, died in France's Gironde region when the storm cut electricity powering her breathing machine
A woman was crushed by a door in Burgos, Spain
A collapsing wall killed a woman and a falling tree killed a male park employee in the Barcelona area; a man, 60, was killed elsewhere in the Catalonia region
In Galicia, a policeman was killed by a falling tree as he directed traffic in Burela and a sailor from a cargo ship died when the vessel got in trouble off the coast
A falling wall crushed a man in Aigues de Busot, near Alicante in the south-east of Spain
Tens of thousands of homes have been left without power in Spain.
French weather agencies had forecast the storm but it affected a wider area than expected. A state of "red alert" was declared in nine departments, but lifted by the end of Saturday.
People were screaming on the street below, and bits of masonry and scaffolding continued to fall
Simon Ritchie BBC News website reader in Rodez, France
The storm caused havoc from the Dordogne area to the Pyrenees. Torrential rains caused flooding in some areas prompting thousands of calls to the emergency services.
The force of the storm also led to the closure of airports in Bordeaux, Pau, Biarritz and Toulouse, and train services also ground to a halt, leaving several hundred passengers stranded in stations. Many roads were also blocked.
Mark Richardson, a BBC News website reader visiting Bordeaux from the UK, said the city ground to a standstill following the storm overnight and felt like a ghost town.
Another reader, Simon Ritchie, witnessed the damage wrought by the storm in the French town of Rodez.
"This morning, I awoke to the sound of very strong winds and lashing rain or hail," he said.
"I looked out of my kitchen's skylight window to see scaffolding and sheets or corrugated iron blowing of the adjacent cathedral. One such sheet blew about 50 yards from the tower and landed on a car below, smashing it in completely."
"People were screaming on the street below, and bits of masonry and scaffolding continued to fall," he added.
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