His remains were found at Waterfoot beach in County Antrim in November.
Mr Wilson was 21 when he went missing from his West Belfast home in 1973. He is believed to have been abducted and murdered by the IRA.
The Independent Commission for the Location of Victims Remains began searching the beach following a tip-off that remains were buried there.
Members of the Wilson family had just attended a walk at Stormont in memory of the Disappeared on 2 November when a call came through to say his remains had been found.
His sister, Anne Connolly, said it was a shock to learn recently that he might be buried in Waterfoot as her mother, Lily, who died three years ago, often sat on the beach in the village.
She spoke of a "mixture of relief, and great sadness" to learn that his body had been found so soon after the dig began.
The remains of eight people have been recovered since the creation of the independent commission by the British and Irish government in 1999.
An inquest will begin on Friday into the death of Peter Wilson, one of the "Disappeared".