However, the name does not refer to any local river; it is a tribute to Brazilian diplomat José Paranhos, Baron of Rio Branco, who negotiated the definitive borders of Brazil and Uruguay.

It is located at the east end of Route 26, about 86 kilometres (53 mi) east-southeast of the department capital city of Melo.

The Yaguarón River (Portuguese: Rio Jaguarão), which forms the natural border with Brazil, flows along the city's northern limits.

Right across the river lies the Brazilian town of Jaguarão, with the Baron of Mauá International Bridge joining the two cities.

On 31 August 1915, the villa (town) previously known as Artigas was given its present name by Act of Law 5330.