Orozco-Estrada was born in Medellín, Colombia, on December 14, 1977. He began his studies on the violin at the city's Instituto Musical Diego Echavarria Misas but switched to conducting when he was 15. At first, he studied at the Pontifical Xaverian University in Bogotá, and then, at 20, he moved to Vienna, Austria, and enrolled at the Hochschule für Musik und darstellende Kunst, taking courses with Uroš Lajovic. Orozco-Estrada remained in Vienna, married, and settled there permanently, eventually becoming a dual citizen of Colombia and Austria. He served as music director of Austria's Oper Klosterneuburg from 2005 to 2007. A breakthrough in the orchestral field came when he conducted the Tonkünstler Orchester Niederösterreich at the Vienna Festwoche as a last-minute substitute in 2004. That led to an appointment as the orchestra's assistant conductor and then, in 2009, as principal conductor, remaining in that post until 2015, He also served as the principal conductor of the Orquesta Sinfónica de Euskadi from 2009 until 2013.
While holding these posts, Orozco-Estrada amassed a strong record as a guest conductor, appearing with the Vienna Philharmonic, the Leipzig Gewandhaus Orchestra, and the City of Birmingham Symphony Orchestra, among other groups. He continued to conduct the Tonkünstler Orchester even after stepping down as chief conductor, and in 2010, he made his recording debut with that group, leading a performance of Mahler's Symphony No. 1 in D major (Titan) on the Preiser label. In 2013, having guest-conducted the group several times, he became the principal conductor of the Frankfurt Radio Symphony Orchestra (the hr-Sinfonieorchester). His contract there was extended through 2021. In 2014, he also took on the post of music director of the Houston Symphony, remaining there until 2022. In 2016, Orozco-Estrada signed with the PentaTone Classics label and recorded a series of albums, mostly with the Frankfurt Radio Symphony and the Houston Symphony. Keen on working with young musicians, Orozco-Estrada also became the principal conductor of the Filarmónica Joven de Colombia and led that group on a tour of Europe in 2019. He frequently conducted the Vienna Symphony Orchestra as a guest, and he spent the 2021-2022 season as its chief conductor-designate. In 2022, however, hearing that the orchestra did not plan to extend his initial contract, he resigned. With the Houston Symphony, he issued an album of music by composer Jimmy López in 2022. ~ James Manheim, Rovi