Police believe the grave is that of an 11-year-old boy who died in 1921.
They found a grave in the city of Humble that had been disturbed, but were still investigating the rest of the teens' story, Houston police Sgt. John Chomiak said.
CBS affiliate KHOU-TV in Houston reports that police do not have any physical evidence yet to confirm the story, but felt confident to pursue charges based on statements from the three teens.
Kevin Wade Jones, 17, and Matthew Richard Gonzalez, 17, both of Kingwood, were arrested Wednesday night and were being held on misdemeanor charges of abuse of a corpse, Chomiak said. A 16-year-old was referred to the Harris County juvenile justice system.
A woman who answered the phone at Gonzalez's home declined comment. A telephone number for Jones could not immediately be found, and it wasn't clear from court records if either had an attorney.
Police were interviewing Jones about the use of a stolen debit card when he told them about the grave theft, which purportedly occurred around March 15, according to court documents.
Gonzalez confirmed the story to investigators in a follow-up interview. Police were led to a heavily wooded site in Humble where they found a knocked-over headstone and water-filled hole more than 4 feet deep. At the time, the muddy water did not allow police to see if the coffin had been disturbed.
"They dug into this gravesite and that was enough to warrant the abuse of corpse charge," Chomiak said. "There has to be further investigation into the actual gravesite."
Preliminary reports indicate the grave was part of a 19th-century veterans cemetery, Chomiak said. While residents in the area knew of the cemetery's existence, it did not appear to be maintained.