It used to be administered as part of the county borough of Teesside , then the county of Cleveland , and it is now in the unitary authority of the Borough of Middlesbrough . Historically part of the North Riding of Yorkshire , in 1968 the town became the center of the County Borough of Teesside , which was absorbed by the non-metropolitan county of Cleveland in 1974 . In 1996 Cleveland was abolished , and Middlesbrough became a unitary authority , within the ceremonial county of North Yorkshire .