Alamo, 74, faces a maximum sentence of 175 years in prison, the Texarkana Gazette reported. He is likely to face spending the rest of his life behind bars.
Some of Alamo's victims, who were not publicly identified, were in the courtroom to hear the verdict. They hugged each other and wept.
"You really appreciate the courage that they showed stepping up to face their demons," said Thomas Browne, the FBI special agent in charge.
Investigators said Alamo, born Berni LaZar Hoffmann, abused the trust his followers had in him. Alamo, whose Alamo Christian Ministries has preached that the Roman Catholic Church and U.S. government are both tools of Satan, blamed the charges against him on a conspiracy led by the Vatican.
Alamo and his second wife founded the Tony and Susan Alamo Christian Foundation in Los Angeles in 1969 after he tried for several years go launch a music career.