Forecasters said up to 6 inches of rain was expected in Hispaniola, the island shared by Haiti and the Dominican Republic.
"Flooding, mudslides, and the rainfall certainly are going to be the biggest problems," said Daniel Brown, a hurricane specialist at the National Hurricane Center in Miami.
At least 15 provinces in the Dominican Republic opened temporary shelters and residents of low-lying areas were urged to seek higher ground.
At 10 a.m. EST, Olga was centered near the eastern tip of the Dominican Republic, about 130 miles east of Santo Domingo, the capital, and it was moving west, the National Hurricane Center said.
Forecasters expected the storm to weaken as it moves across Hispaniola's mountains.
Some areas in Puerto Rico received up to 7 inches of rain.
The Atlantic hurricane season officially ended Nov. 30 but Brown said it is not unusual to have a storm form in December.
Olga will be included in the tally for the 2007 season, bringing the number of named storms to 15, including six hurricanes. The next season officially begins June 1.
In 2005, the busiest Atlantic hurricane season on record, Tropical Storm Zeta formed Dec. 30 and meandered over the Atlantic for about a week without approaching land. Zeta was the 28th and final named storm of that season.
