He studied composition at the National School of Music of UNAM (National Autonomous University of Mexico) and went on to advanced studies in France and Spain. Numerous cultural institutions of Mexico have commissioned works from him, and his music has been published, performed, and recorded in Mexico, Australia, France, Poland, Venezuela, Costa Rica, Brazil, and the United States.
Ibarra's production embraces works in every genre: chamber music, ballets, symphonies, songs, and theater music. He is also one of a very few composers in Mexico today writing opera, sharing that distinction with Marcela Rodriguez and Daniel Catan. Ibarra has served as director of the composition workshop at the CENIDIM (National Center for Music Research and Diffusion) and now directs the composition workshop at the National School of Music of the UNAM.
He has received grants from FONCA (National Foundation for Culture), and from the US-Mexico Exchange Residency Program (1994), and is a member of the National System of Creators of Art. Among his many prizes and awards are the Silvestre Revueltas Composition prize (1975 and 1976); the Lan Adomian award (1980), the Mozart Medal (1991), the National University prize (1993).
Abroad, he was awarded first place in the International Composition contest of Ibague City (Colombia, 1991) and the Jacinto and Inocencio Guerrero award for Best Lyric Work (Madrid, Spain, 1991). In December of 2001 Ibarra was awarded one of Mexico's highest honors, the Bellas Artes award.