Moyzes was born into a musical family in 1906 at Kláštor pod Znievom, Austro-Hungarian Empire.

On its foundation he was appointed professor of composition at the Bratislava Music Academy, where he taught no less than three generations of Slovak composers.

He headed the Academy as Rector from 1965 until 1971, and over the years undertook many important functions in the musical life of his country.

With Eugen Suchoň and Ján Cikker, Alexander Moyzes is considered one of the three leading composers of his generation in Slovakia.

He succeeded in creating a style of composition that was thoroughly Slovak in inspiration, yet nevertheless took account of contemporary trends in European music, a synthesis that he was to consolidate in his later years.