Pope Francis accepted his resignation, as the Vatican press office announced on Saturday.
No reasons were given in the communiqué.
At 71, Dziega has not yet reached the usual age limit of 75 for bishops to resign.
From the end of 2020, allegations of cover-ups against bishops in Poland made headlines.
The churchmen are said to have kept child sexual abuse by clergymen under wraps.
In particular, the case of a priest from the western Polish archdiocese of Szczecin-Cammin caused outrage.
At the beginning of the 1990s, the priest allegedly abused four boys at an orphanage.
According to the accusation, the church had known about it since 1995 but had done nothing about it.
The accused died at the beginning of 2021 after suffering from cancer at the age of 58.