Ríos was born at the Huichicura hacienda, near the town of Cañete, a coal-mining village in the Arauco Province of southern Chile. He was the youngest son of Anselmo Ríos, a rich landowner, and his third wife Lucinda Morales. His father (aged 69 to his young wife's 19 at marriage) died when he was very young so he and his three brothers were raised single-handedly by his mother. He completed his primary studies at the rural school of Cañete, and his secondary studies first at the Liceo of Lebu and later at the one in Concepción, and continued legal studies at the courses given at the annex of his school. Ríos became a lawyer in 1914 with an exposition on the creation and development of the police in Chile.
A member of the conservative wing of the Radical Party since his high school days, he was elected local president of the youth branch of that party and later city councillor. During the presidential election of 1920 he campaigned for Arturo Alessandri, being responsible for the southern part of the country. He was rewarded by Alessandri with the appointment of Consul-general and Chargé d'affaires to Panama. On October 21, 1921 he married Marta Ide, and together they had three sons: Juan, Carlos, and Fernando.
Ríos returned to Chile in 1924, to run in that year's congressional elections. He was elected as deputy for Arauco, Lebu and Cañete, and was reelected in 1925. After Alessandri's return to power following the Chilean coup of 1925, he participated of the committee charged with drafting a new constitution, that led to the approval and proclamation of the 1925 Chilean Constitution.
In the meantime, Juan Antonio Ríos had become president and one of the principal leaders of the Radical Party. During the administration of Luis Barros Borgoño he was elected as President of the Chamber of Deputies.