More than 30 provinces in Spain were put on high alert. The storm later moved into southern France.
One French forecaster was quoted by local media as saying the storm was the worst in the region since 1982.
A man died in his home in the Spanish province of Avila after being hit by flying roof tiles, local officials said on Monday.
A homeless woman froze to death near Valencia, a municipal official told Reuters news agency.
One man was killed in a car accident on a snowbound road in the Asturias region, while another man was found dead outside his home in the town of Moixent with signs of hypothermia.
Social media users in Spain have been publishing footage of flooded streets in Valencia and other cities and towns in Spain.
Spanish forecasters on Monday reported winds of up to 115km/h (71mph), and huge waves on the Mediterranean coast.
Alicante airport was forced to close, resulting in the cancellations of many flights.
What about France?
Storm Gloria has arrived in Pyrénées-Orientales, France's southernmost Mediterranean department, which has been placed on high alert.
Dozens of extra police and firefighters have been deployed in the region.
The A9 motorway on the French side of the border was closed as a precautionary measure.
Gloria was the worst storm to have hit the region in the winter period since January 1982, Météo France forecaster Olivier Proust told Franceinfo.
Spain and France were also hit by heavy flooding in October last year.