Joost was born in the Estonian capital of Tallinn on June 22, 1980. He began music lessons at age six and, after showing unusual talent, was enrolled in a special music school in Tallinn. Joost attended the Estonian Academy of Music, studying orchestral and choral conducting as well as voice (he is a countertenor). For graduate study, he attended the Hochschule für Musik und darstellende Kunst in Vienna and then earned a master's degree from the Royal College of Music in Stockholm in 2008. In Stockholm, he studied with the noted conductor and teacher Jorma Panula. He won prizes at the Jorma Panula Conducting Competition in 2012 and the Malko Competition for Young Conductors in Denmark in 2015. Those honors led to appearances with various ensembles around northern Europe, including the Deutsches Symphonie-Orchester Berlin, the Stuttgart Chamber Orchestra, the Danish National Symphony Orchestra, and the MDR Leipzig Radio Choir, where he served as the artistic director from 2015 to 2019. Joost has also served as the artistic director of the Tallinn Philharmonic Society and has directed Estonia's Birgitta Festival. He is a co-founder of the music theater ensemble Kamber and the noted choir Voces Musicales. Joost has a large repertory of operas and serves as the conductor-in-residence at the Estonian National Opera. In 2020, he became the music director and chief conductor at the Vanemuine Theatre in Tartu, Estonia.
Joost is active on recordings as both an orchestral and a choral conductor. He has made several recordings of music by Estonian composers Arvo Pärt and Tõnu Kõrvits but has also conducted western European music. Several of his recordings were made with the Tallinn Chamber Orchestra, of which he served as chief conductor from 2013 to 2019; with that ensemble, he released two albums of Kõrvits' music in 2020. ~ James Manheim, Rovi