He was an opera and zarzuela composer.
Arrieta founded the Zarzuela Artistic Society and the Teatro de la Zarzuela in Madrid, along with Francisco Asenjo Barbier, José Ynzenga, Cristóbal Oudrid, Rafael Hernando, Joaquín Gaztambide, Luis de Olona and Francisco Salas.
Arrieta’s most famous work is his opera Marina (in 3 acts), composed in 1871. He collaborated with writer Antonio García Gutiérrez, who wrote many librettos for Arrieta’s musical compositions.