Corey Johnson, 40, is charged with felony criminal mischief.
Galveston police say officers started to receive calls Saturday morning about someone throwing concrete and other debris at drivers in the 4100 block of Broadway.
Police increased patrols in the area and found Johnson around 3 p.m., shortly after concrete, wood and pieces of headstones were discovered across several lanes of Broadway.
Johnson was taken into custody on an unrelated charge of drinking in public while Galveston police investigated.
Staff from the City of Galveston Parks Department, the group that runs the historic cemetery, told authorities they've found some 80 headstones damaged over the past month.
He was then connected to the cemetery damage. Johnson's bond was set at $80,000.
Some of the damaged headstones date back to Galveston's antebellum period. The damage is estimated at $13,300.