Bishop Vangheluwe, 73, said the abuse had happened when he was a simple priest and continued when he started as a bishop, a Vatican statement said.
The Vatican said Pope Benedict XVI had accepted the resignation.
The Catholic Church has come under severe pressure over child sexual abuse allegations emerging across the world.
"When I was not yet a bishop, and some time later, I abused a boy," Bishop Vangheluwe said in a letter that was read out at a press conference in Brussels.
"This has marked the victim forever. The wound does not heal. Neither in me nor the victim."
The letter added that Bishop Vangheluwe had repeatedly asked for forgiveness. He had been bishop of Bruges since 1984.
He "repeatedly asked for forgiveness," but didn't bother admitting anything or doing anything about it until worldwide pressure scared him into doing so. How big of him.