Ostojich began officiating in the Primera División in Uruguay in 2013.[2] In 2016, he was included on the FIFA International Referees List for the first time.[2] He officiated his first CONMEBOL club fixture on 11 August 2016 in the Copa Sudamericana in a match between Sol de América of Paraguay and Jorge Wilstermann of Bolivia.[3] The following year, he officiated his first match in the Copa Libertadores, a group stage meeting between Brazilian club Grêmio and Chilean club Deportes Iquique on 12 April 2017.[4] Ostojich officiated his first senior international fixture on 16 November 2018, a friendly match between Argentina and Mexico.[5] The following year, he was selected as a referee for the 2019 Copa América in Brazil,[6] where he officiated a group stage match between Bolivia and Venezuela.[7]