The Vatican said in a statement that Cox, 85, and Ordenes, 54, were "dismissed from the clerical state" by the Pope after having been subject to an investigation by the Congregation for the Doctrine of the Faith, Efe news reported.
The two former bishops will not be able to appeal the decision.
This comes after the defrocking of two other Chilean priests, Fernando Karadima Fariña and Cristian Prech, in the last few weeks.
Cox, who has been accused of committing sexual abuse against minors in Chile, retired in 2002 and has been living in the German town of Vallendar.
Recently, Cox was once again accused of committing sexual abuse in Germany.
After the first accusations against Cox were revealed in Chile, he was sent to live a life of "silence, prayer and penitence" in a German monetary in 2002.
Fernandez then retired and has been living in Peru.
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