The son of José María Ríos Moreiro and Maria Cristina Garcia Martin, he was taught by his parents, who were teachers.
When the family moved to Madrid, he attended St. Maurice School and the IES San Isidro, being always the valedictorian.
He held the positions of Director of the School of Statistics at Complutense University of Madrid, Director of Consejo Superior de Investigaciones Científicas (CSIC) (Superior Council for Scientific Research), Director of the Department of Statistics at the Faculty of Mathematics at the Complutense University of Madrid, and president of the Spanish Statistics and Operations Research Society.
Rios published a Spanish language description of the Von Neumann–Morgenstern utility theorem.
He conducted research with or directed theses of 16 professors, and some directors in statistical bureaus of Latin America.