The southern Caribbean islands of Aruba, Bonaire and Curaçao are under a tropical storm watch.
The National Weather Service forecast model projects the storm to continue northwest through Tuesday and Wednesday toward the northeastern tip of Colombia. Some areas could receive more than 10 inches of rain.
Meanwhile, Storm Team 8 is monitoring another tropical system that has prompted a Tropical Storm Warning to be issued for part of the Louisiana Coast.
Double flag conditions have been declared for Walton County beaches, with officials closing the water to swimmers.
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A tropical storm warning is in effect for Barbados, St. Vincent and the Grenadines, and tropical storm conditions are possible by Tuesday.
Rain had already started to fall along the coast, with more - possibly much more - expected over the next few days. Tropical Storm Arlene formed in late April, becoming only the second tropical storm to form that early in the year in the satellite era, National Hurricane Center forecasters said.
It had maximum sustained winds of 40 miles per hour and was moving northwest at 9 miles per hour. Maximum sustained winds for Bret are at 40 miles per hour.
Bret is the earliest named storm on record to form in the Atlantic Main Development Region (MDR), with storms typically developing in the western Caribbean and Gulf of Mexico this early in the season.
The centre of Tropical Storm Bret was located by an Air Force Hurricane Hunter aircraft to be near latitude 9.4 North, longitude 59.8 West at 5:00pm Monday. A tropical storm watch has been issued for west of Cameron, LA, to San Louis Pass, TX.
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