The man's body was found on the beach at Whitby last weekend
The force says it is now in a position to name the man as 64-year-old Christopher Batty from Whitby .
Officers are appealing for anyone who knew Mr Batty and who saw him between Tuesday January 7 and Saturday January 11 to contact them, as they may hold information which would assist officers.
On the day he was found, Mr Batty was wearing dark blue trousers and a khaki coloured lightweight jacket, which he may have been wearing with the hood up.
Anyone who can help should call the North Yorkshire Police control room on 101, select option 1, and quote reference number 12200005826.
He was found dead close to the east pier on Whitby beach on Saturday January 11.
Police and ambulance vehicles had been spotted on Henrietta Street in the seaside resort, which lies at the foot of the cliffs where St Mary's Church and the Abbey are located.
Police say Mr Batty’s death is not being treated as suspicious, however officers are conducting inquiries to determine his last know movements.