As the fifteenth named storm of the 2003 Atlantic hurricane season, Odette formed near the coast of Panama a few days after the official end of the Atlantic hurricane season ended on November 30, and ultimately made landfall on the Dominican Republic as a moderate tropical storm, before becoming extratropical on December 7, dissipating two days later.

By November 30, the last day of the Atlantic hurricane season, a stationary front extended across eastern Cuba into the southwestern Caribbean.

On December 1, a low-pressure area developed within the frontal zone just north of Panama,[1] and an anticyclone aloft produced good outflow over the low-level center.

Convection increased and became better organized as a weak tropical wave reached the area, and it is estimated the system developed into Tropical Depression Twenty at around 1200 UTC on December 4 while located about 345 miles (555 km) south of Kingston, Jamaica;[1] initially, the depression was forecast to track north-northeastward and pass over western Haiti.

[6] Upon being classified as a tropical cyclone, the depression was embedded within the southwesterly flow between a ridge over the eastern Caribbean Sea and a mid-latitude trough, which caused a steady east-northeast motion.

[7] After being named, the storm intensified despite moderate southwesterly wind shear, and an eye feature became evident on microwave satellite imagery.

The eye feature diminished as the convective structure deteriorated slightly, and hurricane hunters first flew into the storm at around 1200 UTC on December 5.

[1] Odette tracked over an area of warm sea surface temperatures,[8] and the overall cloud pattern gradually improved;[9] the Geophysical Fluid Dynamics Laboratory predicted the storm to attain hurricane status.

[10] Early on December 6, a TRMM overpass showed an 80% closed eyewall,[11] and at 0600 UTC Odette attained peak winds of 65 mph (105 km/h) while located about 245 miles (394 km)/h) southwest of Santo Domingo, Dominican Republic.

[1] Upon reaching peak intensity, Odette had begun accelerating northeastward, which decreased wind shear and slightly increased its southwesterly outflow.

Failing to maintain vertical organization, Odette weakened slightly and made landfall on Jaragua National Park, in the Pedernales Province of the Dominican Republic, around 2300 UTC on December 6 with winds of 60 mph (95 km/h).

[12] Prior to Odette's predicted arrival, the Dominican Republic government issued for the evacuation of more than 10,000 people, mostly from those living near rivers.

[13] A tropical storm watch was issued between Santo Domingo and the Dominican Republic/Haiti border on December 4, 56 hours prior to landfall.

Winds from Tropical Storm Odette were relatively light across the Dominican Republic, with a peak gust of 60 mph occurring in Santo Domingo.