He began his studies with his father Mateo Albéniz, a notable church musician in Spain.

He furthered his education in Paris, where he was instructed by eminent teachers and received musical advice from Rossini.

Returning to Spain in 1830, he served as organist at the Church of Santa María in San Sebastián and then became a professor at the Madrid Royal Conservatory, organist of the Capilla Real, and the personal piano teacher of Queen Isabella II.

Later in life he neglected his career as a concert pianist and dedicated himself instead to teaching.

He left behind many compositions for piano, chamber music and songs, but was subsequently remembered chiefly for his piano method, which was studied by all Spanish pianists at the Madrid Conservatory during the mid-19th century.