As the Vatican announced on Saturday, Pope Francis accepted the resignation.
Dziuba had been Bishop of Lowicz in central Poland for 20 years.
According to Polish press reports, the Vatican had initiated an investigation against Dziuba in 2020.
It concerned whether he had acted in accordance with church law in several cases in which priests from his diocese were accused of sexually abusing minors.
State investigations too
The investigation was carried out by the responsible Metropolitan Archbishop of Lodz, Grzegorz Rys.
He forwarded the results to the Vatican.
In 2022, a Polish state commission of enquiry also launched an investigation on suspicion of failure to press charges against Dziuba.
According to the Vatican embassy in Poland (Saturday), an investigation into the Dziuba case revealed "difficulties in the administration of the diocese".
In particular, it concerns "failures in dealing with cases of sexual abuse committed by individual clergy against minors".
Bishop Dziuba, who has now resigned, was the personal secretary of the politically influential Cardinal Jozef Glemp, who was Primate of Poland, from 1984 to 1998.
At the Catholic University of Lublin, Dziuba headed the Department of the History of Moral Theology.
He was also director of the study centre on Cardinal Stefan Wyszynski (1901-1981) in Warsaw.