Pope Benedict XVI accepted Vangheluwe's resignation, under a canon law provision for "illness" or unspecified "other serious reasons", the Vatican said.
'Culture of secrecy'
A number of other bishops have resigned since scandals involving catholic priests began sweeping Europe and the Americas last November.
On Thursday, the pope also accepted the resignation of Irish Bishop James Moriarty, named in a damning report that found Catholic authorities in the Dublin archdiocese concealed abuse of children by priests for three decades.
The resignation of Moriarty, also 73, was the fourth to be approved over the scandal in Dublin, Ireland's biggest archdiocese.
The investigation found church leaders there did not report abuse to police until the 1990s as part of a culture of secrecy and an overriding wish to avoid damaging the reputation of the Catholic church.
One priest admitted to sexually abusing more than 100 children, while another confessed that he had abused children on a fortnightly basis over 25 years.
Similar revelations across the world have rocked the Roman Catholic church, and one of Germany's most senior bishops, Bishop of Augsburg Walter Mixa, offered his resignation to the pope on Thursday after admitting he beat children at a Catholic orphanage in the 1970s and 1980s.