Alex made landfall on the island of Terceira as a storm with 70 mph winds, the National Hurricane Center said. By late morning, Alex was 35 miles north of Terceira and was maintaining that direction.
"Little change in strength during the next 48 hours is forecast, and Alex is expected to lose tropical characteristics later today," the National Hurricane Center said on Facebook.
About 250,000 people live on the nine islands of Portugal's Azores,
which is home to a U.S. airbase at Lajes Field. It saw "limited" damage in the storm and gave an all-clear notification, according to its website.
The event is the fourth known storm to arrive in the first month of the year since forecasters began keeping track in 1851.
The fact that Alex had hurricane strength at all is surprising because tropical storms thrive most over warm waters, something that's unexpected in the North Atlantic in the middle of winter.
The water was indeed cool -- about 68 degrees Fahrenheit -- but the air was super cold at minus 76 degrees. The 144-degree difference helped give the storm enough energy to be a hurricane, CNN meteorologist Chad Myers said.
The Atlantic hurricane season officially runs from June 1 to November 30, but that doesn't mean tropical systems don't pop up at other times, although it is infrequent.
Alex is not just the first named storm of 2016, but it's also the first named storm to form in the Atlantic in January since 1978.
About 900 miles from Europe and 2,300 miles from the United States, the Azores are marked by rolling green hills and volcanic peaks. The archipelago, which Portuguese navigators discovered uninhabited in 1427, has a subtropical climate, with temperatures hovering year-round between 57 and 71 degrees F.
The storm was expected to dump 3 to 5 inches of rain on the islands, with 7 inches possible in isolated areas. That precipitation could spur mudslides and flash floods, while dangerous storm surges could produce flooding along the coast.
There's no expectation Alex will directly strike the United States or Europe. Instead, it will likely head north toward Greenland.