He stressed the apology was a follow up to the regret expressed by the dying Bishop Sheil when he revoked his excommunication of Mary in 1872, The Southern Cross reports.
Speaking at the blessing and dedication of the Blessed Mary MacKillop statue and plaza in Victoria Square, Archbishop Wilson pointed out that the excommunication was, in fact, invalid and that he was "profoundly ashamed of the Bishop's actions in driving the Sisters out onto the streets."
"This statue will stand as a sign of our affection and as an act of reparation for what happened so long ago," he said.
"The centenary year of Mary's death is a time of great celebration and we want to repair any hurt we have caused in the past in the spirit of reconciliation and forgiveness."
A number of Josephite Sisters attending the ceremony wept as the Archbishop made the apology.
Sr Marion Gambin, Leader of the South Australian Province of the Sisters of St Joseph in South Australia, said it was a very moving experience.
"It was very unexpected and quite humbling," she said.
"We are really very grateful and a lot of the Sisters have expressed their gratitude."
She said the excommunication had caused much anxiety and many sisters had ended up homeless.
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