Costa started his F1 career as the chief designer for Minardi in 1988 and became the technical director in 1989 after Giacomo Caliri, ex-technical director of the team, left. Costa joined the Scuderia Ferrari in 1995 and in 1998 became assistant to the team's Chief Designer, Rory Byrne. When Byrne announced his intention to retire in 2004, Costa was named as his successor. Byrne credited the design of the 2005 Ferrari to Costa.
Before the 2006 season, Aldo Costa was promoted to be the Head of Design and Development at Ferrari, as the team announced Nicholas Tombazis as their new Chief Designer. On November 12, 2007 Ferrari announced that Aldo Costa will take on the role of technical director.