The route was designated on February 20, 1942. On September 26, 1945, SH 345 was rerouted to end at FM 106 east of Rio Hondo, rather than directly in Rio Hondo.
On February 20, 1942, the route was established. However, on September 26, 1945, SH 345 was changed to end at FM 106 east of Rio Hondo rather than directly in Rio Hondo.