The jogger discovered the bag at 9:30 a.m. Tuesday, the Houston Chronicle reported. He dragged the bag to his home and discovered it contained 25 bricks of cocaine, packaged in plastic wrap and rubber.
The man recognized the packages as cocaine from television programs and called the police.
Each brick weighed one kilogram (2.2 pounds) and tested positive for cocaine.
Galveston police Capt. Jeff Heyse said the owner of the drugs probably either tossed the bag overboard after sighting a U.S. Coast Guard boat, or the bag was intended to drift to the beach for pickup.
"We'll never know, unless a body washes up behind it," Heyse said.
The drugs were being sent to FBI lab to determine a country of origin.