Cornelius Burgh studied law and music in Cologne. From 1616 to 1618, he was employed as an organist by the Benedictines of Mönchengladbach at the ''Münsterkirche''. In 1618, he married Eva Aredtz in Mönchengladbach and moved with her to Erkelenz, where he worked as a notary, lawyer, and organist at St. Lambertus Parish Church. His two daughters, Catharina (born in 1618) and Anna (born in 1621), were born in Erkelenz.
Due to his main profession, Burgh began composing late in life. In 1626, he presented his collection ''Liber primus concertum ecclesiasticorum'', consisting of 20 three-part sacred concertos. In his collection ''Hortus Marianus'', published in 1630, consisting of 25 four-part sacred concertos, he used exclusively Marian texts. His models were the works of composers such as Claudio Monteverdi, Lodovico Grossi da Viadana, and Alessandro Grandi, which were associated with the monody that was flourishing in Italy at the time and the emerging basso continuo music. Burgh's works were distributed in the Rhineland and the Spanish Netherlands.