The section named Morrison Drive was constructed in the early 1950's. It was named for William McG. Morrison, mayor of Charleston from 1953 to 1954.
The eastern terminus is near the historic wharves of Charleston, including Adgers Wharf, which is now the site of a playground. It is also adjacent to the old Exchange, or Customs House, of Charleston. The current Customs House that was built around the time of the Civil War is on this route.
When Morrison Drive was constructed, there was still one private terminal operating near the Eastern terminus, the Clydeline Steamship Company. The Clydeline terminal burned down in 1955. In the late 80s, the land of the terminal was rebuilt as Charleston Waterfront Park.