He studied at the State Conservatory under Zdeněk Bílek - the last of Václav Talich's students and continued his studies at the Academy of Performing Arts in Bratislava under the pedagogical guidance of Ondrej Lenárd. He has been working at the Slovak National Theatre since 2006. From 2013 to 2016, he was the music director of the Prague State Opera. Leginus was the primary guest conductor of the Prague Chamber Orchestra in the 2015/2016 season and has conducted at major concert halls such as the Vienna and Berlin Konzerthaus and the Bunka Kaikan in Tokyo. Conducting twenty performances of Verdi's La Traviata, he completed a successful Japanese tour with the Prague State Opera in October 2015. From 2018 to 2022, he was a permanent guest conductor of the State Chamber Orchestra in Žilina. In 2022, he staged Dvořák's Rusalka at the Teatr Wielki in Poznań. Martin Leginus has conducted the operas Orfeo and Eurydice, Carmen, The Magic Flute, Barbier of Seville, The Two Foscari, Macbeth, La Traviata, Aida, Nabucco, Otello, Simone Boccanegra, Rigoletto, Falstaff, Don Carlo, Hansel und Gretel, Cavalleria Rusticana, The Comedians, Madama Butterfly, La Boheme, La Rondine, Manon Lescaut, Tosca, Il Tabarro, Gianni Schicchi, Suor Angelica, The Bartered Bride, Rusalka, Martin and the Sun, Svätopluk and the ballets The Swan Lake, Sleeping Beauty, The Nutcracker, Spartacus, Ivan the Terrible, Romeo and Juliet, Sylphide, Giselle and Cinderella. He has collaborated with several important soloists such as Leo Nucci, Ferruccio Furlanetto, Simon Keenlyside, José Cura, Iwona Sobotka, Anna Samuil, Desirée Rancatore, Jana Kurucová, Pavol Breslik, Adriana Kučerová, Sergej Larin, Dalibor Jenis, Eva Hornyaková, Peter Mikuláš, Eva Urbanová and others.
Martin Leginus has been the Slovak National Theatre Opera director since 2023.