Ordenes, 47, was the youngest bishop to be ordained in Chile and the first Chilean bishop to be investigated by the Vatican, The Santiago Times reported.
Pope Benedict XVI accepted his resignation Tuesday, the Vatican office in Chile announced.
An investigation began four months into charges brought by Rodrigo Pino in 2008 that Ordenes had abused him when he was a child.
Ordenes said he had a "reckless act" with Pino when his accuser was 17 and not considered a minor.
In an interview with a Chilean newspaper, Ordenes said he regretted the incident and apologized for it shortly afterward.
Ordenes said he offered to resign when questioned about the allegations in April, but the Vatican did not accept.
Pablo Lizama Riquelme, the archbishop of Antofagasta, will assume Ordenes' duties until a successor is appointed.