Lord Mulholland said: “This is a very serious charge. Stabbing them with a knife and the victim bleeding to death.
“There will be an inevitable lengthy sentence of imprisonment.”
He deferred sentence for reports to the High Court in Livingston on 6 January.
Wilson was remanded in custody.
Det Insp Gavin Fleming, the senior investigating officer with Police Scotland, said: “This was a shocking and violent attack that resulted in the horrific death of a much-loved young woman.
“While this conviction cannot change what has happened, I hope it brings some kind of closure for Sarah’s family and friends, who remain absolutely devastated by what has happened.”
