Police Scotland state that Abdelnabi Alainani, aged 30, who was picked up on CCTV after leaving the Dumfries facility, was found in the Humberside town on Saturday.
He is now said to be being cared for by police and NHS staff in Scunthorpe.
National appeals were issued after Mr Alinami’s disappearance.
A major search operation was launched after the patient left the hospital, located close to the Crichton Business Park.
The focus of the search switched to Humberside after a lorry driver, who travelled from Dumfries, reported seeing a man fitting Mr Alimani’s description getting out of his vehicle in Scunthorpe.
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