Rivero Weber studied in the National Music Conservatory of Mexico with Luz Maria Puente, in the Curtis Institute of Music (Philadelphia, USA) with Jorge Bolet, graduating in 1984, and in the State Conservatory of Odessa (Ukraine) with Ludmilla Guinsburg, a collaborator of the great teacher Henrich Neuhaus.

In 1984, Rivero Weber obtained the Diploma di Merito de Accademia Chigiana (Siena, Italy), where he studied with Guido Agosti. He has performed as a soloist and accompanist in Mexico, the U.S., France, Italy, Austria and the former Soviet Union. As a soloist, some of his most imporant performances were with the Sinfónica Nacional de Mexico, Sinfónica de Mineria, Filarmónica de la Ciudad de México, Filarmónica de la Universidad Nacional Autonoma de México, Sinfónica del Estado de México, Orquesta de Cámara de Morelos, Sinfónica Carlos Chávez and the Curtis Symphony Orchestra, among others, under the baton of such great conductors as Bátiz, Diemecke, Herrera de la Fuente, Zollman, Sánchez-Zuber, Medina, Neshling, Nanut, Gati, Greenburg and Aito. Rivero Weber has participated in radio and television programs, stage productions and festivals like the Internacional Cervantino, the Cultural de Sinaloa, Idiart, the cycle “The glory of the piano”, the Foro Internacional de Música Nueva Manuel Enríquez, among others.

Rivero Weber has made five recordings of Mexican, European and Latin American music for piano, as well as one of music of the German philosopher, Freidrich Nietzsche. He was professor and coordinator of the piano department of the Escuela Superior de Musica of INBA (Instituto Nacional de Bellas Artes) until 1995. He has been distinguinshed on two occasions with a scholarhips from the Fondo Nacional para la Cultura y las Artes. He was one of the artistic representatives of Mexico in the Expo-Lisboa 98, where he presented a concert of Mexican music. He was the National Coordinator of Music and Opera at INBA.

Currently he is the Director General of Music in the Universidad Nacional Autonoma de Mexico (UNAM).