The Tropical Storm Warning which had been in effect for Jamaica since 6:30 on Tuesday morning has been discontinued.
The warning has been discontinued as Grace continues to move further away from the island.
In its latest advisory issued just after 5:00 this morning, the Meteorological Office said the center of Grace is located at 280-kilometres or 175-miles west-northwest of Negril Point Jamaica.
Grace is 45 miles South East of Grand Cayman.
The system is moving at 26-kilometres per hour and is expected to pass over the Cayman Islands this morning.
Grace is then expected to approach the Yucatan Peninsula of Mexico tonight into Thursday morning.
Maximum sustained winds have increased to 65 miles per hour with higher gusts.
Tropical Storm Grace is expected to become a Hurricane tonight before it approaches the Yucatan Peninsula.
In its final bulletin issued on Grace this morning, the Met Service of Jamaica said the large area of showers and thunderstorms associated with they system has moved away from the island.
Weather conditions are expected to return to normal today.