Michael Errington is currently serving 18 years in prison for manslaughter and has spent the last nine years living at The Priory Hospital in Darlington.
The 51-year-old left the secure unit on Friday on approved leave but failed to return.
Police issued a ‘do not approach’ warning for Mr Errington who caught a train to Edinburgh, arriving into Waverley at 2.38pm on Saturday where he was captured on CCTV getting off the train.
It was believed he had not taken his medication since Saturday and without it he could become aggressive and unpredictable.
Police have now confirmed Mr Errington was traced in the St Leonards area of Edinburgh at around 2.30pm today.
A spokesman said: "We can confirm that 51-year-old Michael Errington was traced in the St Leonards area at around 2.30pm this afternoon.
"Thanks to everyone who shared our appeal. We continue to liaise with colleagues from Durham Constabulary."