White's descendants played prominent political and economic roles in Knoxville's development for more than a century after his death. His eldest son, Hugh Lawson White, was a United States Senator, and ran for president on the Whig ticket in 1836. Along with Charles McClung, White's sons-in-law included Judge John Overton (married to Mary White), a cofounder of Memphis, Tennessee, and Senator John Williams (married to Melinda White). His other descendants include Congressman Joseph Lanier Williams, railroad magnate Charles McClung McGhee, Admiral Richmond P. Hobson, and playwright Tennessee Williams.