Alexander Rüth studied conducting, church music and school music at the University of Music and Dance Cologne. In addition to his studies, he worked as a church musician in Refrath, as deputy director of the Cologne Men's Vocal Performance Association, and as musical assistant for the German Youth Chamber Choir, the national selection ensemble of the German Choral Association.

In 2011, Alexander Rüth came to Würzburg as cathedral cantor. During this time, he developed in particular the Girls' Choir at Würzburg Cathedral into a highly qualified choir. Among the outstanding projects under his direction are intercontinental concert tours to Venezuela, the USA and Canada, various radio and CD productions as well as large choral symphonic concert performances, also in combination with semi-staged elements and in educational formats for children and young people.

In 2021, Alexander Rüth assumed the position of Minster Music Director at the Constance Cathedral (Archdiocese of Freiburg). There he directed all ensembles of the Minster Music and was entrusted with all musical activities at the former cathedral church on Lake Constance. In addition, he was involved as a board member in the festival management of the Constance Choral Festival.

On September 1, 2022, Alexander Rüth was appointed Cathedral Kapellmeister at the Cathedral Church of St. Kilian in Würzburg. He thus has overall responsibility for Dommusik Würzburg, one of the largest and most important institutions of its kind in Germany, with its ensembles: the Girls' Choir, the Cathedral Boys' Choir, the Cathedral Choir, the Chamber Choir, the Vocal Ensemble and the Choralscholen. Through the new formation of the Junge Domkantorei, Alexander Rüth expanded the choral landscape at the cathedral to include a mixed youth choir, which under his direction is dedicated to the development of special musical projects.

Since 2017, Alexander Rüth has been teaching choral conducting at the State University of Music and Performing Arts in Mannheim. In addition, he holds a teaching position for children's choir conducting/choral pedagogy at the University of Music in Würzburg and is active as a lecturer for various choir associations.