Several Indigenous names are recorded: Korkoranna for Morgan itself, Koolpoola for the opposite flats, and Coerabko ('Katarapko'), meaning meeting place, for the bend locality.

The town was proclaimed in 1878, the year the railway line from Adelaide via Kapunda was opened, and was named at that time after Sir William Morgan, then Chief Secretary, later Premier of South Australia.

Just southward (downstream) from Morgan is a riverfront development named Brenda Park, which has flourished since WWII, originally as rustic shacks, but now as prestige waterfront holiday homes.

Morgan is in the Mid Murray Council local government area, the state electoral district of Stuart, and the federal Division of Barker.

During World War II, the Morgan-Whyalla pipeline was built from the Murray River at Morgan to supply fresh water to the city of Whyalla.