Leslie had been downgraded from a category one hurricane to a post-tropical cyclone with winds of 110 km/h by the time it landed on Portugal's Atlantic coast late Saturday.
Leslie was located 580 miles (935 km) east of the Azores as it produced maximum sustained winds of 75 mph, the NHC said.
The Category 1 hurricane is expected to produce unsafe winds, surf and heavy rainfall in Portugal and Spain on Saturday night and Sunday, the center said.
Governor Ralph Northam today declared a state of emergency in anticipation of impacts from Tropical Storm Michael.
The storm was the most intense overnight bringing localised flooding and uprooting thousands of trees.
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Meteorological records indicate that only five hurricanes have ever arrived in this part of the Atlantic Ocean, and Leslie could turn out to be the fiercest storm to hit Portugal since 1842.
Spain was also expected to be hit by the severe weather, dubbed a "zombie" storm because it first formed on 23 September and has meandered through the Atlantic Ocean for weeks.
Spanish meteorologists expected Leslie to reach Spanish mainland territory early Sunday before weakening to a tropical storm.
In October 2017, strong winds from Hurricane Ophelia, which travelled north off the coast of Portugal and western Spain, fed forest fires that killed around 40 people during a heatwave.
Leslie moved east yesterday across the Iberian Peninsula to Spain, where authorities issued warnings for heavy rains and storm conditions for the northern part of the country, advising Spaniards to avoid driving in the storm.