Southwest Ordinance on May 26, 1790, out of land that was ceded to the U.S. federal government by North Carolina; it passed from existence with Tennessee's admission to the Union on June 1, 1796.
The name "Territory South of the River Ohio" suggests a much larger territory than modern-day Tennessee. Even though Kentucky was south of the Ohio River, it was still a part of Virginia when the Southwest Territory was organized in 1790, and it would stay part of Virginia until it became a state in 1792. The land south of modern-day Tennessee was either still claimed by Georgia or disputed with Spain. Part of it would be organized as the Mississippi Territory in 1798, two years after the Southwest Territory had passed from existence.
The Southwest Territory is not the same as the modern Southwestern United States.