Tombazis graduated with a degree in engineering in 1989 at the Trinity College in Cambridge, followed by a PhD in aeronautical engineering at the Imperial College London in 1992.
In November 1992 he became aerodynamicist at the Benetton Formula 1 team and was promoted to Head of Aerodynamics in 1994. Three years later he moved to the Scuderia Ferrari, where, in 1998, he became Head of Aerodynamics and CFD. In 2004 he went back to England, to work with McLaren, where he started working in a similar position and being promoted to Head of Planning.
In March 2006 he was back at Ferrari, this time as Chief Designer. He left Ferrari on 16 December 2014.