Vincent Inametti, 48, faces a maximum sentence of 10 years in prison and a $500,000 fine after pleading guilty in federal court to two counts of sexual abuse of a ward, U.S. Attorney Richard B. Roper said.
Inametti, who remains free on bond, is to be sentenced in March.
Authorities received a complaint earlier this year that Inametti was having sex with one inmate at Federal Medical Center Carswell, and further investigation revealed that he was involved with two women. Both were serving federal sentences for drug distribution conspiracy convictions.
One inmate met Inametti in 2004 after attending church services and becoming involved in the choir and Bible study classes, authorities said. The other met the priest a few months later after being assigned as a clerk for the prison's religious services department.
In documents filed in court Wednesday, Inametti admitted that last year he told one inmate to meet him in the chapel library, and the two had sex. He said that also last year, he told the other inmate to meet him in a classroom in the chapel, where they had sex.
Days earlier Inametti's attorney, Mike Heiskell, told CBS News affiliate KVTV that his client has committed no crime. "This is simply a case of two willing adults, two consenting adults, being accused of having intimate activities in the wrong place at the wrong time."
Prison officials say there is a 'zero tolerance' policy against any sexual activities with inmates.
Inametti worked at FMC Carswell about seven years. He is a naturalized U.S. citizen who was ordained in his native country, Nigeria, according to documents filed in the case.