The U.S. National Hurricane Center in Miami said Saturday that Bud had degenerated to a remnant low. It was expected to dissipate within the next day or say.
Maximum sustained winds had weakened significantly and were near 30 mph (48 kph) as the storm hovered about 15 miles (24 kilometers) off the coast of Cabo Corrientes, Mexico.
Forecasters say the storm could still drop another inch or two of rain along Mexico's southwestern coast.
Bud had brought driving rain earlier Saturday, leaving emergency officials on high alert for flooding and mudslides.
All tropical storm warnings and watches have now been discontinued.