Brendan is from Humberside.
Following enquiries and a search supported by the Coastguard, Mr Carrier was located safe and well on the A171 near Whitby at 1.30am on Sunday (16 December).
He has been transported back to Hull.
Police say they are grateful to the media and members of the public who supported the appeal.
There are serious concerns for his welfare as he left without his medication, he was only wearing a shirt and jeans and he has no means to pay for accommodation.
Brendon is known to enjoy living outdoors but the freezing conditions pose an increased risk.
While the initial police searches and enquiries have concentrated in the Wetherby area and his home in Humberside, it is known that Brendon enjoys travelling around the UK and abroad.
Places in the UK that he has recently visited include Whitby in North Yorkshire, London and Aberdeen in Scotland.
All police forces and travel hubs in the country have been notified about the missing person appeal.
Anyone with information about Brendon Carrier or have possibly seen a man matching his description since Friday evening, please contact North Yorkshire Police without delay on 101, option 1, and speak to the Force Control Room. Please quote reference NYP-14122018-0565.