The defrocked priest, 68, died Saturday after being attacked by a fellow inmate with a white supremacist past, officials said.
Prosecutors said they plan to charge Joseph Druce, 37, with murder. Druce is already serving a life sentence for a 1988 murder.
An autopsy on Geoghan was planned for Monday. He was convicted last year of indecent assault and battery in the first of three criminal cases brought against him.
"The Archdiocese of Boston offers prayers for the repose of John's soul and extends its prayers and consolation to his beloved sister, Cathy, at this time of personal loss," said Father Christopher Coyne, a spokesman for the archdiocese.