Nicene and Post-Nicene Fathers, Ser. II, Vol. XIV:
The Canons of the Councils of Ancyra, Gangra, Neocæsarea, Antioch and Laodicea, which Canons were Accepted and Received by the Ecumenical Synods.: Canon XXIII

Canon XXIII.

It shall not be lawful for a bishop, even at the close of life, to appoint another as successor to himself; and if any such thing should be done, the appointment shall be void.  But the ecclesiastical law must be observed, that a bishop must not be appointed otherwise than by a synod and with the judgment of the bishops, who have the authority to promote the man who is worthy, after the falling asleep of him who has ceased from his labours.

Notes.

Ancient Epitome of Canon XXIII.

A dying bishop shall not appoint another bishop.  But when he is dead a worthy successor shall be provided by a synod of those who have this power.

Nothing could be more important than the provision of this canon.  It is evidently intended to prevent nepotism in every form, and to leave the appointment to the vacant p. 120 see absolutely to the free choice of the Metropolitan and his synod.  The history of the Church, and its present practice, is a curious commentary upon the ancient legislation, and the appointment of coadjutor bishops cum jure successionis, so common in later days, seems to be a somewhat ingenious way of escaping the force of the canon.  Van Espen, however, reminds his readers of the most interesting case of St. Augustine of Hippo (which he himself narrates in his Epistle CCXIII.) of how he was chosen by his predecessor as bishop of Hippo, both he and the then bishop being ignorant of the fact that it was prohibited by the canons.  And how when in his old age the people wished him to have one chosen bishop to help him till his death and to succeed him afterwards, he declined saying:  “What was worthy of blame in my own case, shall not be a blot likewise upon my son.”  He did not hesitate to say who he thought most worthy to succeed him, but he added, “he shall be a presbyter, as he is, and when God so wills he shall be a bishop.”  Van Espen adds; “All this should be read carefully that thence may be learned how St. Augustine set an example to bishops and pastors of taking all the pains possible that after their deaths true pastors, and not thieves and wolves, should enter into their flocks, who in a short time would destroy all they had accomplished by so much labour in so long a time.”  (Cf. Eusebius.  H. E., Lib. VI., cap. xj. and cap. xxxij.)

Compare Apostolic Canon number LXXVI.

This canon is found in the Corpus Juris Canonici, Gratian’s Decretum, Pars II., Causa VIII., Quæst. I., can. III., in Dionysius’s version, and again Canon IV. in that of Martin Bracarensis.