It gradually strengthened and was upgraded to a tropical storm on July 17 and crossed the northern Leeward Islands later that day.

As it neared landfall in Puerto Rico early on July 18, upper-level winds weakened it back to a tropical depression.

Claudette remained disorganized and the National Hurricane Center operationally reported that it degenerated back into a tropical wave after crossing Puerto Rico.

Claudette struck western Cuba on July 21, shortly before reaching the Gulf of Mexico and "regenerating" into a tropical cyclone.

By July 23, Claudette regained tropical storm intensity and turned northward toward the Gulf Coast of the United States.

Rainfall exceeding 10 inches (250 mm) in some areas of Puerto Rico led to widespread agricultural damage, flooded homes and streets, and one fatality; losses were estimated at $750,000 (1979 USD).

In Alvin, 42 inches (1,100 mm) of rain fell in one day, which at one point was the record 24‑hour precipitation amount for any location in the United States.

[1] As the storm moved westward, it encountered wind shear, weakening it back to depression status when it hit Puerto Rico.

Claudette moved across islands of Hispaniola and Cuba as a tropical depression before reforming in the Gulf of Mexico on July 21.

Runoff from Blue Mountain caused a normally dry creek bed to overflow, flooding several homes in the Mon Bijou area.

Widespread agricultural damage was reported, especially in Las Marías, Maricao, Sabana Grande, and San Sebastián.

Seven homes and fishing camps were significantly damaged or destroyed by waves and strong winds in Johnson Bayou.

At Constance Beach in Cameron Parish, up to 40 feet (12 m) of sand was eroded along a 1 mile (1.6 km) long section.

Heavy rainfall in Farmington backed-up sewer drains, flooded basements, and blew-off large manhole covers.

[12] On July 28, 1979, President Jimmy Carter issued a disaster declaration for Texas, allowing the counties of Brazoria, Chambers, Dallas, Galveston, Jefferson and Orange to be eligible for government aid in order to recover from flooding.