Nicholas Harper - who has been described as a "brilliant husband and a great dad" - was discovered by a member of the public on Saturday in woodland near Cowhouse Bank car park, Helmsley.
Mr Harper, 50, from Pickering, a former data analyst, had been working on a placement at Archbishop Holgate’s School in York before going missing on February 7, it was reported.
His car was later found at Cowhouse Wood.
Searches of the area took place with the help of Scarborough and Ryedale Mountain Rescue Team and Cleveland Mountain Rescue Team, who joined police dog teams and a force helicopter.
North Yorkshire Police said in a statement: "Although formal identification has yet to take place, Mr Harper’s family have been informed.
"Police do not believe there are any suspicious circumstances surrounding the death."