The US National Hurricane Centre (NHC) said the sub-tropical storm was 785 miles south-west of the Azores, with winds up to 85 mph.
Storm Alex is moving north-east and is expected to hit the Azores on January 15, prompting a hurricane warning.
It is one of the earliest tropical systems to form in the Atlantic Hurricane Basin since records began.
Meanwhile, another tropical storm, Pali, has formed over the Pacific, similarly rare at this time of year.
Scientists have linked the storms to powerful winds and high sea surface temperatures resulting from an unusually strong El Nino phenomenon in 2016.
The World Meteorological Organization (WMO) has said the 2015 occurrence of El Nino will be among the three strongest recorded since 1950.
Severe droughts and significant flooding in many parts of the world are being attributed to the phenomenon, which occurs every two to seven years.
El Nino is a naturally occurring weather episode that sees the warm waters of the central Pacific expand eastwards towards North and South America.
Image source: Wikimedia Commons President-elect Donald Trump celebrated his election victory at the Ultimate Fighting…
Millions of voters across the US chose to return Donald Trump to the White House…
Donald Trump declares victory in the US election as he addresses jubilant supporters in Florida.…
Stocks around the world are rising as Donald Trump appears to be on the cusp…
Donald Trump has won Pennsylvania, North Carolina and Georgia and taken a lead over Kamala…
Quincy Jones, the celebrated musician and producer who worked with Michael Jackson, Frank Sinatra, Ray…