Leslie was downgraded from a hurricane before it reached Portugal late on Saturday. Authorities had urged people to stay indoors and keep away from coastal areas.
At least 1,000 trees were uprooted, mainly in coastal towns north of Lisbon where the storm first reached land, hitting power lines and blocking roads.
The A1, the main motorway running through Portugal, was temporarily blocked by a fallen tree, authorities said.
More than 300,000 homes lost electricity as the storm passed, said Belo Costa, commander at the Civil Protection Agency.
The storm, carrying winds of up 100 km/h (60 mph), was most intense during the night. By Sunday morning the powerful winds and heavy rains had mostly subsided.
In Spain, winds of up to 100 km/h uprooted trees in the center of the country early on Sunday morning. Emergency services issued flood warnings for the north and northwest of the country for Sunday afternoon and evening, advising Spaniards to avoid driving in the storm.
Earlier this week, 12 people were killed in flash floods on the Mediterranean island of Mallorca.
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