"The Holy Father Francis has accepted the resignation of Bishop Kieran Conry from the dioceses of Arundel and Brighton," a statement said.
Conry, 64, had said in a letter to his parishioners that he had veered from the precepts of the Catholic church but underscored that his actions "were not illegal and did not involve minors."
According to reports in the British press, Conry, who was appointed by Pope John Paul II in 2001 as bishop of Arundel and Brighton in southeast England, had an affair with a married woman.
The Archbishop of Southwark Peter Smith has been named the Apostolic Administrator of the diocese until a new bishop takes up the office.
The head of the Catholic church in England and Wales, Vincent Nichols, said it was a "difficult and sad moment".